So here are the results of our research on the Gospel of Thomas. We have two groups of sayings: one was incorporated together into the Markan tradition, by the author of Secret Mark (and hence became triple synoptic tradition), and the other was incorporated together into the Q gospel (which itself derived from Secret Mark, hence already included some of the triple tradition material).
Canonical Mark was then derived from Secret Mark, and was combined with the Q gospel (i.e. the Gospel of Peter) to create the Gospel of Matthew and Marcion's gospel. (Marcion's gospel would eventually morph into the Gospel of Luke, largely based on Marcion's work.)
Here is the group of logia incorporated directly from GTh into Secret Mark--parentheses indicate questionable parallels, a tilde ("~") indicates a similarity to a stronger parallel, and the square brackets indicate an alternate versification.
4:2 (5~)6:5-6 9 (14:4?) (14:5?) 20 (21:9?) 22:1-2(~46:2) 31 33 35 (40?) 41 46b 47 48(~106) 62:1 65 66 71 99 100 104 113
And here is the (much larger) group of logia incorporated directly from GTh into Q:
2 3:1-2 4 8 10 14:4 16 21:5 24:3 26 30 32 33:1 34 36 39:1-2 43:3 45 46a 47:2 54 55 57 58 61:1 61:3 62:2 63 64 68 69 72 73 75 76:1-2? 76:3 78 79 86 89 90 91:2 92:1 93 94 95 96:1-2 101 103 107 109 113
A couple of things to notice right off the bat:
Nearly all of the sayings included by Secret Mark are included in De Conick's "Kernel Gospel", those GTh sayings found in what she believes to be the first layer of GTh. The exceptions are: 14:5, 22:1-2, 106, and I only include 14:5 and 106 tentatively. Let's deal with each in turn.
14:5--earlier I noted that this falls within the so-called "Bethsaida" section of GMk. I think this section was missing from Secret Mark--hence was missing from the Q-gospel--hence was discarded by Marcion as suspect, only to be added back into Acts by Luke when he used the Matthean/Hebrew tradition to revise Marcion's gospel. So it's possible 14:5 was added into canonical GMk by Mark independently of GTh.
It's also possible that an earlier version of 14:5 was present in Secret Mark, and was moved by Mark to the Bethsaida section. Personally I favor this alternative, but I admit it is just a hunch; I have no evidence for it. Thus I include 14:5 in the group of Markan sayings only with strong reservations; it may resemble Mk 7:15 only due to oral tradition (as De Conick suggests).
22:1-2--De Conick puts all of logion 22 into material belonging to later layers of GTh. In the case of 22:2 specifically, she points to several scholars who have described the "little one" as the "androgynous primal Adam". But this is to conflate 22:1-2 with 22:3-7. True, the latter section turns into a discussion of spiritual androgyny. But 22:1-2 by itself makes no such connection. The "little ones" are simply infants, nothing more. They are their own metaphor. 22:1-2 is most likely a kernel saying, with 22:3-7 a later accretion.
Furthermore, De Conick begins by saying "Development [i.e. inclusion in a later layer] is indicated by the dialogue format." But 22:1-2 are the portion of logion 22 prior to the dialogue. Hence, they can easily represent a kernel sayings, only later developed into a dialogue. De Conick should have included logion 22:1-2 in her kernel sayings.
106--this is a parallel with 48. 48 is indisputably kernel material. 106 may be a doubling of it, as De Conick suggests. I concur, and only include 106 in the first group for the sake of completeness. It's more likely that the Secret Mark author used logion 48, rather than 106, but it's possible that one or the other is the original, or that the Secret Mark author used both.
As for the list of sayings added by the Q author, they amount to nearly (though not quite) half of GTh. If you also consider the sayings already found in Secret Mark, and carried into the Q-gospel, arguably a majority of GTh sayings are found in the Q-gospel. So it's not entirely inaccurate to call GTh...proto-Q.
So it looks like the Secret Mark author used a couple of dozen kernel sayings from the original Gospel of Thomas, i.e. the "kernel sayings" as De Conick describes them. The Q-author then revised Secret Mark for his own purposes, as well as a revised GTh, adding nearly half of the sayings he found in his revised GTh.
And that's how GTh worked its way into the synoptic tradition.