At trainer speeds, it shouldn't be a problem. I wouldn't worry about it.

If you disconnect the control linkage, does the elevator droop under it's own weight? If you invert the plane, does it then fall the other way under it's own weight? In theory, that is what should happen. But CA hinges usually add a bit of resistance to the surface. And if one of them is off by even a hair, it can cause the flex you are seeing.

Oh, do make sure that the stab isn't cracked or anything like that. It's possible for the covering to basically hold a cracked stab together, and the only think you'd see is a little flex like you are talking about. Until you pull hard-up, that is. Ask me how I know

(actually, I caught my plane (not a trainer) that had that problem on the ground, but only after flying it and thinking that the elevator response "felt wrong" that day. It looked and felt ok on the ground, but I went home anyway, and checked more carefully in the shop. I was lucky, the built-up stab had a cracked main spar and would have let go before too long).