Whatever it is there for, it is not like the screw some of the CVA and Traditions locks have to adjust the depth of the full cock notch.
I actually was so interested in your pictures that I took my TC Hawkens lock out of the stock and studied it. If I'm seeing this correctly, the half cock notch looks like it is completely broken off. That explains the area below the little shelf that is what is left of the half cock notch with the broken looking metal under it. If it is, your gun cannot be set to half cock.
Putting that screw where it is could keep the sear from engaging the full cock notch as deeply as TC designed it to do.
In that location, if the screw was adjusted so it did not stick out of the surrounding surface, it would do nothing.
If it was backed out so the hex end was standing proud of the surrounding area far enough, the forward side of the sear would bump into it. This would keep the nose of the sear from being able to go completely down into the full cock notch.
I haven't seen many TC locks but the ones I have seen don't have anything like this screw in them. I would guess that someone annealed (softened) the tumbler, drilled and threaded the hole and then rehardened the tumbler.
If they didn't temper the tumbler after it was hardened, that would easily explain why the half cock notch on the lock is broken.
In any case, using the gun with that tumbler in it is dangerous. I strongly suggest that you get a new tumbler for your gun.