I'm embarrassed to admit this since I feel like I've seen GF1&2 countless times. I never noticed that when Carlo gets into the car about to be strangled by Clemenza, there is a brief cutaway right before showing Tom jerk his tie as to let Clemenza know "go ahead."
Should I be ashamed?

That was Tom just loosening his tie on a warm day. Clemenza had his orders before he got in the car with Carlo.

Exactly TB. Tom is walking behind Rocco who is walking behind Michael. Thus, Tom is not even to the gate yet. Clemenza is sitting in the back seat of a hardtop on the street side of the vehicle and it's unlikely he has any view of Michael or Rocco, let alone Tom. Of course, the mall is occupied with Mafiosi, so what's the point of a signal.

As you state TB: Clemenza had his instructions.

I agree that Tom wasn't trying to give any signal. Everyone there knew what was going to happen beforehand except for Carlo.

If you look at Tom's face while he loosens his tie you can tell he looks troubled. Although Tom had been around the life since he was a child you can tell he's still not comfortable with murder. When Sollozzo tells Tom "I know you're not the muscle end of the family" earlier in the movie it drives home the point that Tom isn't a killer. When Tom says "It's almost 1946 nobody wants bloodshed" it again shows he isn't comfortable with the idea of murder like others in his circle are.

In contrast Michael's face is cold with that killer stare when they walk out of the house. The way Al stands behind Carlo when he's sitting in the chair inside, you can tell Al is just hoping for Carlo to say something stupid so Al can rip his head off. Even the way the guy who escorts Carlo out and opens the door looks as if he's ready to whack the guy right there. And then Clemenza with his sarcastic "Hello Carlo" when he gets in. They are all willing and ready to whack the prick.

To me the loosening of his tie along with the look on his face, is a nervous reaction and shows how uncomfortable he is with what is happening. He is literally trying to breathe easier.

It is simply brilliant foreshadowing of what was about to happen next to Carlo considering he was about to have trouble breathing himself.

Yes. In the novel, just after Michael says he'll kill Sol and Mac, Tom "...looked glum, the statesman forced to go to war. 'At least we know what we're going to do.'"

Tom did the same loosening of his tie, when Tessio was being taken away to be killed