What is the proper way to remove these rings ? They are on an old weaver 2.5 power so the front one is obvious, and the rear will come off if you unscrew the ocular but should you do that?

In the days before nitrogen-filled scopes, taking them apart for mounting was not unheard of. Those old steel German scopes with claw mounts had to be completely stripped before the claw bit could be soldered on. Then the surface had to be refinished and blued again.

PS: if you have to take the ocular housing off, do it in front of an airconditioner that's going. I've noticed that this can reduce humidity from 60 or 70 per cent to 40 per cent.