as i understand this, you are caring for your neighbor's cat. the neighbor doesn't let the cat inside because the cat sprays, is that right? so, does the woman take care of the cat at all? feed it or keep it warm at night? if the cat gets sick, will she take it to the vet? does she want the cat, because it sounds like the cat might now be yours. before you worry yourself sick over this, find out if the woman really wants the cat. maybe the cat really does belong to you.
if the cat belongs to you, you might slowly start to bring it in. whatever the reason was that it sprayed before, it may be fine with you. some 'marriages' aren't made in heaven, and the cat-neighbor one may be one of those. but you might be the perfect match. since it seemed interested in your cat through the window, it may want cat company, who knows? but find out first who owns that cat - you or she. no misunderstandings later.