You mean your class-specific hunting log?

You can finish that at anytime you're strong enough to kill the mobs - even at level 50 (or level 80 for that matter), but as you noticed: you wont earn exp from it if you finish hunts when your character has reached max level (so 50 if you didnt buy any expansions, up to 80 with Shadowbringers active on your account).

I think I finished my hunting log for puglist somewhat around level 68? It even still gave me the fixed amount of exp, though that obviously didnt really matter at that level anymore.