I was thinkin of how often T.H.E.M. is mentioned in this season's Sam and Max. In way, it reminds me of Hugh Bliss's cult in season 1, where it is at least mentioned in the background or in dialogue at least once per episode.
My theory is that the organization is more like a group of villains, much like S.p.e.c.t.o.r. (I think that is what they are called) in the 007 movies or the Legion of Doom/legion like in Superfriends/DC universe.
I'd imagine that the acronym is probably a team members name and that each member are shown in each episode, whereas they all get together in episode five. I mean, there are four words in them and five episodes.
If I am correct, I can imagine the Moai being the M or the giant red Triangle being the T
The posessed Santa could be H as in Hell or something.