There is absolutely nothing you can do to damage the t-stat when turning off the power (under any sequence), unless you short out a wire on the control circuit (ie.removing wire nuts, or shorting a terminal to ‘common’).
As for dirty filters; I am currently looking for an R22 scroll compressor because a tenant didn’t change a ‘high efficiency’ filter. She figured she bought a better filter and didn’t need to change as often. It flooded the compressor with refrigerant and broke the shaft to the scroll (something that is uncommon in a scroll).
Flooding a scroll generally does not do damage like in a reciprocal, but washing out the oil from the compressor will kill it.
If I see a dirty filter I can’t see through, it stays out.
You should always document this because it may fail as soon as you walk out the door.