there's no easy way to check if a Time Turner has been used other than to see if it can still be used

If the turner also has a restriction[1], it’s easy to check: just ask someone not important to try to use it. (Not important in the sense that it’s no big deal if they loose the ability to time-turn for a day).

[1:] It should have. They can be broken/destroyed, which suggests that they can also accumulate non-fatal damage (like scratches), which technically means that they also carry information to the past. But the information rules don’t seem to apply except when in some cases involving sentience.