Well, I may not have the exact reason why, the sanitizer have penetrated the wood and darken it in that spot, which I would expect, to have been from the inside of her hand.
You may need to CA the whole wood before mounting it and seal the wood from any possible penetrations from other liquids however, if you want to save that ring, I suggest you soak it into the same sanitizer that created the stain, I would actually remove gently the CA surface of the outer part of the wood to help the sanitiser penetration to be more consistent.
I suppose, what I'm trying to say is that, you can try to have the wood to look all the same this way, and then CA it again however, I'm not sure in any future contact with sanitiser or any other chemical, is not going to penetrate the wood again and change the wood appearance, again...!
I would think that, you may get better results by using the super thin CA to apply multiple coats on the wood before mounting it in the metal frame, you can only try and see what happens...!
Cheers
George