Are you positive this cat is owned by this neighbor, or maybe just being fed out of kindness?? I would talk with her and see if she really wants the cat. If she says she does and is still not providing a good home maybe you could take it in and if you don't want to keep it, at least find a home. This may not seem like the right action, but in my opinion if the cat is neglected and uncared for they don't deserve to own it.