But I have not a clue why their memories would disappear.
Give it up. You're trying to explain something that can't be explained. Forget what you saw on the screen and think about what happened
has the pilot and the sergeant on board. They slingshot around the Sun and travel backwards the day or two to when they first arrived. If they try to beam the pilot into the cockpit before they tractor the plane, it will get real crowded in there with two pilots, one of them a day or two older than the other. If they beam him in after he had been beamed up, then the pilot—a day or two older and unluckier—ends up in a plane that is breaking up. How does any of this erase the Enterprise's
If we assume the paradox worked, then there'd be no reason to beam the sergeant back, because he never would have met Kirk and Sulu. So what happens to the guy they have on board?
Again, it is all nonsense. There is no logic to explain. The classic example is called the "grandfather paradox." Imagine you build a time machine, travel back to before your own father is conceived and kill your grandfather. What happens? None of this could happen because if you kill your granddad before your own father is conceived, you
will never be born to grow old enough to build a time machine and commit suicide in this bizarre fashion.
Forget all notions of changing history (paradox) or time "happening again." Traveling back to a time you had already experienced does not make any of it "happen again," and your older double would have been there "the first time around" anyway. That's why I mentioned "Assignment Earth." The Enterprise
crew didn't know that they were part of the history they were observing.