If it brings her joy to look at and try on her rings, then let her be. Who is she hurting by doing this behaviour? It is probably a bit OCD, but if it gives her something to do, and she's not hurting anyone, then so be it.
If you don't want her going into her room throughout the day, perhaps you can bring her jewelry box out into the living room closer to her, so she doesn't have to keep going back and forth.
If this is your major problem with caring for your mom, count your blessings. Things could be much worse.
OCD and paranoid behaviors are very common with dementia/Alz., unfortunately. Leave your mom's rings in a jewelry box where she can have easy access to them; that's the best you can do. That way, she can go into her room 100x a day if she'd like and feel comforted to see that they're in their usual spot, safe and sound (providing she doesn't want to wear them on her hands where she can see them 24/7).
If you don't want her going into her room throughout the day, perhaps you can bring her jewelry box out into the living room closer to her, so she doesn't have to keep going back and forth.
If this is your major problem with caring for your mom, count your blessings. Things could be much worse.
Good luck!
If she is not terribly confused, would she be willing to leave her rings on her fingers for a longer part of her day?
Would she let you keep them for her in a “safe place” accessible through you at any time that she wanted them?
If you think she is beyond taking gentle suggestions, could you purchase a set of rings that she would accept as a substitute?
Unfortunately this is pretty familiar territory for many people for whom their rings were the greatest treasure they ever received or would ever own.
My MIL was mugged in a hospital parking lot years ago, and one of the losses was her engagement ring, set with a small diamond.
When we asked her why on earth it was in her purse instead of on her finger she answered “Because I was afraid someone would try to steal it from me”.
Hope you find a gentle solution.