|Baptism of Christ, 3rd century, Catacomb of Callixtus|
There is a lot to unpack here. Marcionite priority, as can be seen in the diagram to the right, does not imply Marcion or Marcionites originated the New Testament writings, rather that they were the first to package Christian writings in forms like those we have today, and also (in my opinion) were the first sect to use these writings for evangelical purposes.
The things to keep in mind here: Mark does not know the Marcionite gospel, nor does he know Matthew, he knows only two versions of the prototypes. Matthew knows the Marcionite gospel and a version of the prototype which was on of the two used by Mark, and the Marcionite gospel knows only the other prototype gospel that is shared with Mark.
So if John the Baptist was introduced by the Marcionite author, then Mark should not know about him. But in fact he does. Therefore stories about John must predate the published gospels, including the Marcionite, and must have been in the prototype gospels. But was John's baptism of Jesus in those gospels, specifically "L" the version shared by Mark and Marcion?
John in Marcion:
To answer that question we need to examine the passages of John in the Marcionite gospel to determine where they came from. The first question to ask is, was John know as a baptizer to the Marcionite author? And a quick look at the evidence shows that indeed John is known as the baptizer to the Marcionite author.
We see John referred to as the Baptist in the Question of Authority (Luke 20:1-8), a story attested in Marcion. Although we cannot say exactly what the full wording of the story was in Marcionite form, we do have a some paraphrased snippets preserved by Tertullian (AM 4.38.1-2) confirming the passage and the reference to John's Baptism.
Christ knew "the baptism of John, (baptisma Ioannis) whence it was." (Luke 20:4) Then why did He ask them, as if He knew not? He knew that the Pharisees would not give Him an answer; then why did He ask in vain? Was it that He might judge them out of their own mouth, or their own heart? Suppose you refer these points to an excuse of the Creator, or to His comparison with Christ; then consider what would have happened if the Pharisees had replied to His question. Suppose their answer to have been, that John's baptism was "of men," they would have been immediately stoned to death. (Luke 20:6) Some Marcion, in rivalry to Marcion, would have stood up and said: O most excellent God; how different are his ways from the Creator's! Knowing that men would rush down headlong over it, He placed them actually on the very precipice. For thus do men treat of the Creator respecting His law of the tree. But John's baptism was "from heaven." "Why, therefore," asks Christ, "did ye not believe him?" (Luke 20:5) He therefore who had wished men to believe John, purposing to censure them because they had not believed him, belonged to Him whose sacrament John was administering. But, at any rate, when He actually met their refusal to say what they thought, with such reprisals as, "Neither tell I you by what authority I do these things," (Luke 20:8) He returned evil for evil! Ignoring the polemic arguments of Tertullian, we see John is associated with baptism, a baptism account not in the Marcionite Gospel. And if we consider why the question of authority of Jesus would even be tied to the question of John's baptism and it's authority, we come to realize it is the the baptism of Jesus which in view here. Quite simply did John baptize Jesus with authority from the heavens, as depicted in Mark 1:9-11
In those days Jesus came from Nazareth  of Galilee and was baptized by John in the Jordan. And when he came up out of the water, immediately he saw the heavens opened and the Spirit descending upon him like a dove; and a voice came from heaven, "Thou art my beloved Son; with thee I am well pleased."Since John baptized Jesus, to accept that John's baptism was from heaven would be to accept Jesus as the one, the Christ, whose baptism by John was from heaven. To say the baptism is from men would be to say Jesus's authority is not from heaven either. The two authorities are inextricable related. And there is no other reason for the passage than their being intertwined. But these authorities are also tied to the concept John as Elijah come again from the Malachi prophecy, and of John endorsing Jesus - an anathema to the Marcionites.
The evidence is more explicit from Dialogue Adamantius 2.13 when the Marcionite champion Markus quotes Luke 9:18-20 (slightly paraphrased)
In the Gospel Christ says, "'Who do men say that I, the son of man, am?' The disciples said, 'John the Baptist; but some say Elijah; while others claim that one of the prophets of old has arisen.' And he said to them, 'But who do you say?' Peter, answering, said, 'the Christ'" (τὸν Χριστόν / Tu es Christus)The presence of this passage in Marcion is confirmed in AM4.21.6, where Tertullian says Jesus asks Peter "Whom do you say that I am?" quisnam illis videretur (Luke 9:20) and he replies "You are the Christ," Tu es Christus, and then 'He commanded them "to tell no man that saying"' ille autem praecepit ne cui hoc dicerent (Luke 9:21).
Tertullian report vouchsafes Adamantius' snippet as basically accurate. So we can safely say that the Marcionite author knows and refers to John as "John the Baptist" (Ἰωάννην τὸν βαπτιστήν), and he knows of the Elijah come again motif and it's association with John, and also that of the old prophets. Importantly these are tied up with who Jesus is.
There is no escaping it, these passages of involving John in Marcion (see Luke 9:18-22 and 20:1-8) depend upon the Baptism scene. So what happened to it?
Marcionite Gospel Opening:
When we look at the Synoptic Gospels, discounting the clearly additive infancy stories, they begin with the appearance of John the Baptist, some form of the temptation in the desert and the calling of the fisherman stories. If we assume Mark essentially preserved the basic order, we see that Marcion's Gospel begins at the same place as Mark 1:21 (Luke 4:31) with only the additional prefix "In the fifteenth year of Tiberius Caesar"  as the opening comment to fix the time and location.
So all that is missing are a mere 20 verses in Mark. But as we shall see the actual number of verses lost is much less than that, and in fact almost none when we look at their replacements.
For example, the calling of the fishermen, which we find for example in Mark 1:16-20, has simply been move to after the Capernaum sequence instead of before it, at Luke 5:1-11 (AM 4.5.1). This fits the Marcionite author's purpose of introducing Jesus as descending (κατῆλθεν) into Capernaum, as if from heaven. But it makes sense to have Jesus, and perhaps also Simon, introduced prior to calling his first disciples.
It has long been my argument that Mark 1:1 is nothing more than the versification by prefixing ἀρχή to the title he found, τοῦ εὐαγγελίου Ἰησοῦ Χριστοῦ "The Gospel of Jesus Christ". This verse then was not removed by the Marcionite author, it was instead invented by Mark. Further Mark 1:2-3 we will show later is a conflation of two separate sources, of which the Marcionite knew only one of these of these verses (that is Mark 1:2 less the words ἐν τῷ Ἠσαΐᾳ τῷ προφήτῃ).
A Baker's dozen verses in the prototype gospel our Marcionite author knew have gone missing (see Mark 1:2, 4-15). But as we shall see, these verses were transformed into a new story
Markus Vinzent rightly points out the sequence refuting John actually begins with the resurrection of the widow's only son at Nain (Luke 7:11-17), when the crowd witnessing the miracle proclaim, "A great prophet (Προφήτης μέγας) is risen up among us, and God hath visited His people." 
This appearance of one, held by the masses as a Προφήτης μέγας, who brings the dead back to life is what triggers John to ask, as reported by the Marcionite champion Megethius (DA 1.26):
"Now when he (John) had heard in prison the works of Christ, he sent his disciples to him, saying 'Are you he who is to come, or look we for another?”
ἀκούσας γὰρ ἐν τῷ δεσμωτηρίῳ τὰ ἕργα τοῦ Χριστοῦ, ἔπεμψε τοὺς μαθητὰς αὐτοῦ πρὸς αὐτὸν λέγω· Σὺ εἶ ὁ ἐρχόμενος ἢ ἕτερον προσδοκῶμεν;
Cum audisset in carcere positus opera Christi, mittens duos ex discipulis suis ad eum dixit: Tu es qui uenturus es, an alium exspectamus? 
Tertullian (AM 4.18.6) reports also that John shares the crowds awe at this great prophet saying,
Hoc igitur metu et Ioannes, Tu es, inquit, qui venis, an alium expectamus?
We see here that John Baptism is refuted. How could John have baptized Jesus, seen the spirit descend like a dove from heaven, and hear the voice from heaven declare Jesus his beloved son, and yet not know he was the Christ, the one he was looking for? This would be impossible.
Megethius tells us this was the Marcionite view, as he prefaces the above quotes saying:
I offer you exact proof that the Christ of the Law and Prophets belonged to another: John did not recognize him. For it would be impossible for the prophet of the God of Creation to be ignorant of his own Christ.Tertullian understands this Marcionite position, and spends much of AM 4.18.4ff attempting to argue that not only was John of the law and prophets but that Jesus was too because he baptized him! But he acknowledges the Marcionites had their own detailed explanation (plenum ordinum) to explain this very verse, as Megethius enlightens us.
Tertullian effectively gives us the explanation for why the baptism scene was removed, as it was understood as the direct and explicit connection between Jesus and the God of the Law and Prophets. Further he inadvertently gives away the reason why the Marcionite writer would write the passage of John's ignorance of Jesus, how his first hearing about Jesus would not be a voice from heaven but from his own disciple while in prison, about an unexpected and unknown Christ.
Are are assured it is John's baptism which is rejected, when we compare all the topical elements of the two passages when we compare Luke 7:24-28 to Mark 1:2-14:
The Marcionite Jesus (Luke 7:24, AM 4.18.8) ask this question to the crowds concerning John: "What did you go out into the wilderness (εἰς τὴν ἔρημον) to behold (θεάσασθαι) ?" John in the story is not at this time to be found in the desert here, he is in prison. This Marcionite Jesus is speaking of another scene, the one in found in Mark 1:4-5 when John the baptizer appeared in the wilderness (ἐν τῇ ἐρήμῳ) ... and all those in the region of Judea came out to him.
Jesus then speaks of John's preaching ironically, with the rhetorical follow up question, "A reed (κάλαμον) shaken by the wind (ἀνέμου)?" This "reed" (κάλαμος) is meant as a derisive insult, as it seems to be associated with a supposed rod (ῥάβδος) of power, like used by kings and great prophets, such as when Moses uses it, often via Aaron, brings on the plagues (e.g., Exodus 10:13, also 7:19, 8:5, 8:16-17), and as the staff of God (ῥάβδος τοῦ θεοῦ per Exodus 17:9) and more generally to bring miracles (Number 20:8); and with other prophets such as Isaiah to bring the wrath of God (Isaiah 10:5). We see examples of this derisive insult in Ezekiel 29:6 where the Pharaoh's rod is said to be made of reed (ῥάβδος καλαμίνη) when attempted to be used against the house of Israel. The same imagery appears in Isaiah 36:6 and the identical verse of 2 Kings 18:21, only this time even more like a wet noodle, say Pharaoh's rod is as if crushed reed (τὴν ῥάβδον τὴν καλαμίνην τὴν τεθλασμένην). This is not a king's golden scepter (re Esther 4:11, 5:2, 8:4), but the staff of great prophet's in the wilderness, no place for a king. But this a prophet Jesus ridicules, suggesting his rod, that is his preaching, is a week reed that can be shaken by the winds; something a Marcionite exegete would clearly see as implying the inferiority of John's message and his God. 
The question is repeated,"But what did you go out to see?" (Luke 7:25) but this time the garments of John in the baptism story are in view. The accounts of Mark 1:6 (and parallel Matthew 3:5) we are told John wore a garment made of camel's hair with a leather belt, and that he ate a humble diet locust and wild honey. But this humbleness Jesus chooses to ridicule in his rhetorical reply, "a man dressed in soft (μαλακοῖς) clothing?" This is the opposite of the presentation of John in Mark, and clearly meant to rattle. What says next is even more intriguing, "Behold, those who wear soft (μαλακὰ) raiment are in kings' houses." 
It's a twist for sure. The crowd is either being told John is not the prophet they are seeking or else that John is in one of the kings' houses. Both are possibilities. The latter however could point us back to the beginning of the passage which as reported by Megethius above, "Now when he (John) had heard in prison the works of Christ."  The first thing to note, John's imprisonment is reported in Mark 1:14 (Matthew 4:12), part of the sequence which is missing in the Marcionite Gospel we are examining. But secondly, John's imprisonment in leads to his beheading, an event not to be noted until a few chapters later.  The parallel synoptic accounts are followed by an elaborate description of Herod's birthday party (Mark 6:17-20, Matthew 14:3-12) where John's head is placed on a platter. This very much implies that John was held in Herod's house. Further Herod is referred to in the story as a king in Matthew 14:9 (also Mark 16:22-23, 25-27). The Marcionite text that stood at Luke 7:25 may well have been referring to John being held prisoner, more like as a house guest hostage than in the cellar. Holding important people as a house guest type prisoner in the palace was quite common for those deemed important. This could well be what Jesus' remark alludes to.
The next verse (Luke 7:26-27) the question is asked a third time, "What then did you go out to see?" The follow reply of Jesus,
"A prophet? Yes, I tell you, and more than a prophet. This is he of whom it is written, 'Behold, I send my messenger before thy face, who shall prepare thy way before thee.'"The comparison is clear for Mark 1:2 which speaks of John, saying "as it is written (γέγραπται)," and then quotes Malachi 3:1. Luke 7:27 (AM 4.18.7, Panarion 18.104.22.168) says of John "this is he of whom it is written (γέγραπται)," and then quotes the identical verse, appending "before you" (ἔμπροσθέν σου).  Tertullian explains the "more than a prophet" περισσοτερον προφητου as meaning ἄγγελόν μου, the messenger of the Creator. Or to quote Malachi 3:1 ὁ ἄγγελος τῆς διαθήκης "the messenger of the covenant", that is of the Old Testament. This is precisely from where the Marcionites juxtapose John as the prophet of the Creator, who calls the Jews to repent and return to Law of Moses, the statutes and ordinances that were commanded him (Malachi 4:4), for he is Elijah again per Matthew 11:14 (Malachi 4:5, see Luke 9:9, etc.).
The passage closes with Jesus declaring, "I tell you, among those born of women none is greater than John; yet he who is least in the kingdom of God is greater than he." (Luke 7:28, AM 4.18.8). Parsing this we can see that as elsewhere the Marcionite author juxtaposes John against Jesus. While Jesus descends into Capernaum, presumably coming directly from the heavens, John came into being more naturally, "born of women," which by inference Jesus was not. Further, with the Malachi prophecy, specifically Malachi 3:1, 4:4-5 in immediate view, John is Elijah come again, the greatest prophet (Προφήτης μέγας) of the Jewish God. But even the greatest of the God of Moses' prophets he is less than the least Christian in heaven.  And he becomes aware of his inferiority in the Marcionite account after word of Jesus being a great prophet reaches him, and scandalizes him, leading Jesus to say 'Blessed is he who is not be offended (σκανδαλισθῇ) in me,' (Luke 7:23), directed at John according to both Tertullian (AM 4.18.5) and Epiphanius (P 22.214.171.124).
Conclusions about Luke 7:18-28
It seems clear the Marcionite author was no different from the other gospel writers in respect to his editorial decisions to add and remove material as required to fit his theological requirements. Luke 7:18-28 was written (albeit with text in places more like Matthew's text than Luke's) drawing almost exclusively from Baptism story, largely as we have in Mark 1:2, 4-14. We have seen above references to elements found in 8 of those 12 verses. In effect Luke 7:18-28 replaces the Baptism story in Mark 1:2-11, 14. Only the Temptation story, a mere two verses of Mark 1:12-13, left no trace.
It should be noted that other verses in the Marcionite Gospels were clearly moved from their original setting in the prototype gospel. Examples include the parable of the Mustard Seed, which was moved to the "central sections" at Luke 13:18-19 and likely stood where the True Relatives stood in Luke 8:19-21; The Tricky Question found in Luke 10:25-28 was probably right after the burning bush of Luke 20:37 in the prototype; and other verses as. The Marcionite author was quite willing and adept at moving material when he needed. So moving the calling of the fishermen after the opening Capernaum sequence fits a pattern. The writers of the other Gospels did likewise, save perhaps Mark.
The Marcionite author in this one redaction from the prototype gospel he built upon achieve three goals: John no longer comes before Jesus and no longer endorses him; John's story is refuted and his relationship with Jesus is no longer intimate, in fact he they never meet; the Gospel now starts with Jesus entrance into Capernaum where he is introduced. This proved successful for Marcionite evangelism.
Baptism Scene in the Prototype Gospel L:
As a surprise bonus, our model offers an explanation for how the quote of Malachi got incorrectly attributed to Isaiah in Mark 1:2.
The demonstration that Luke 7:18-22 was written in response to and as a replacement for roughly the first dozen verses of the prototype Gospel known to Mark and Luke, tells us that the writer of Luke 7:27 only knew a version quoting Malachi 3:1. From this I conclude the prototype "L" known by Mark and Luke/Marcion began roughly as follows:
In those days came John the Baptist preaching in the wilderness. This is he of whom it is written, 'Behold, I send my messenger before thy face, who shall prepare thy way [before thee].' (Luke 7:27, Malachi 3:1) And there went out to him all the country of Judea they were baptized by him in the river Jordan, confessing their sins. Now John was clothed with camel's hair, and had a leather girdle around his waist, and ate locusts and wild honey.However the prototype "M" known by Mark and Matthew began something like this:
In those days came John the Baptist, preaching a baptism of repentance in the wilderness of Judea, For this is he who was spoken of by the prophet Isaiah when he said, "The voice of one crying in the wilderness: Prepare the way of the Lord, make his paths straight." (Matthew 3:3, Isaiah 40:3 LXX) Now John wore a garment of camel's hair, and a leather girdle around his waist; and his food was locusts and wild honey. Then went out to him Jerusalem and all Judea and they were baptized by him in the river Jordan, confessing their sins.These two sources invoked two different OT verses to associate with John. The prototype "L", which was known to the Marcionite gospel writer, invoked Malachi 3:1, while the prototype "M", known to Matthew, instead used Isaiah 40:3 to identify John. Mark conflated both versions, and so took both OT quotes. But Mark did not know the OT (that is the LXX) at all. So when he conflated the two verses from M and L he did not know where the OT quotes acme from, so simply accepted the identification from 'M" for the source of both quotes.
It seems clear John the Baptism and the Baptism of Jesus were part of the early prototype gospel. John began the prototype gospel, with the theology of Elijah come again. Even though the Gospel of John rejects the concept of John as a prophet come again, he still kept the baptism of Jesus, albeit in very different form. Only Marcion did not have the baptism scene, but as we demonstrated above his section on John, found at Luke 7:18-28 (albeit reading closer to Matthew at some points), was derived from the baptism scene of the prototype gospel.
The model for Marcionite (published literary) priority holds up. Differences in the gospels over the story of John can almost entirely be explained within the confines of internal Christian sectarian conflicts of the mid 2nd century. The Marcionite author's knowledge and refutation of the baptism scene betrays diversity already within the Christian camp at the moment the first published gospel (the Marcionite) was formed. Further we find the tactics and methods of the Marcionite gospel writer to be of the same sort as the other gospel writers. And finally we find that John the Baptist was not a stray of secondary element which found it's way into the gospels, but part of the background story from the very beginnings.
 There are many other gospel order theories with Marcionite priority, which will not be discussed here. One of the more improbable is put forth by Markus Vinzent, which basically postulates that the prototype gospel was itself a pre-published version of the Marcionite gospel (replaces L, M, and Marcion in my graph) and all the synoptic gospels were written from than with Marcion's gospel written in response. In my view this is the result of his inflating the position of Marcion (based on his overly optimistic assessment of the veracity of the Patristic writers).
 The Marcionite version appears to more closely resemble Matthew 21:25 than Luke 20:4, and it is the Pharisees rather than the Chief Priests, Scribes and Elders who challenge Jesus' authority.
 Nazareth (Ναζαρὲτ) is either a Markan addition to the prototype Gospel account, or more likely a later editorial addition as there is no mention of Nazareth in Mark, and is not part of the story, rather an epitaph for theological reasons outside scope of that Gospel.
 ἐν τῷ πεντεκαιδεκάτῳ ἔτει Τιβερίου Καίσαρος, Epiphanius P42.11.5
 Magnus prophetes prodiit in nobis, et Respexit deus populum suum. Tertullian, AM 4.18.3
 Dialogue Adamantius 1.26, The paraphrase of Luke 7:18-20, essentially reads as Matthew 11:2-3 complete with in carcere (ἐν τῷ δεσμωτηρίῳ). Here we have an example of the Marcionite text preserved in Matthew, and likely revised by Luke.
 This "reed shaken in the wind" (κάλαμον ὑπὸ ἀνέμου σαλευόμενον) closely resembles 1 Kings 14:15 MT "as a reed is shaken in the water" (ינוד הקנה במים). Besides being highly improbable the reference is to this verse as their is no evidence this gospel writer could read Hebrew, and 1 Kings 14:1-20 is not found in the early LXX, and may date from Christian era. So we look to other sources.
The this shaken as being inferior concept is Hebrews 11:26-27, where the things that can be shaken by the voice (a kind of wind) of God are not created (a Gnostic would say from the Creator) and fall away, leaving to remain only those things not shaken, that is not created (i.e., spiritual)
 I follow Matthew 11:8 here, since it's probably closer to the Marcionite text, as Luke has some revision. One of the indicators that the Lukan text has changed are pastoral words like τρυφῇ
 see note 6 above.
 In Luke this occurs at verse 9:9. But this verse is not attested in Marcion and may be a Lukan redaction drawn from the parallel in Mark 6:16, which the Lukan writer felt was sufficient to convey John's death without the story of Herod's birthday party.
 It is quite likely Mark, in conflating his two sources, dropped ἔμπροσθέν σου.
 The reference here to the story of the Rich Man and Lazarus from Luke 16:19-29, but importantly not verses 16:30-31 (from the later Catholic redactor), which terminates in the Marcionite with "They have there Moses and the prophets, let them hear them." Tertullian goes into great detail in AM 4.18.10-13, concerning the Marcionite view that not following Moses and the prophets lands you in Tartarus portion of Hades, while the Elysian fields, i.e., Abraham's bosom, are for those who are the greatest, but these fall short of heaven for those who follow Christ. Christ of course descended into Hades at his death to claim his own, which would be from Abraham's bosom according Marcionite lore. The Jewish or Creator God had already passed judgements on his own separating them in his Heaven (Elysian fields) and Hell (Tartarus). From the Marcionite view, John would reside in Abraham's bosom, the greatest of the Creator's prophets, but would not reside in the High God's heaven (presumably the Pleroma).