Do I have to give a cat back I found a month and a half ago if it was neglected?

While hanging out in a friend's backyard I saw a kitten being tormented by her dog. She was 3-5 months old (has not gone into heat). She told me it was a stray that had been living in her yard for 2 weeks & suggested I take it home. It was full of fleas & it took us 2 weeks to get our other cat adjusted to her (now they're best friends). This was a month & a 1/2 ago. We have fully fallen in love with her. Turns out she wasn't a stray & the owners want her back. A friend had seen her at our house a few times & coincidentally found out his step grandmother's cat had been missing, who lives next door to where we found her. We are fully attached to her now & she is part of our family. Since she was full of fleas and obviously neglected for weeks before we found her, I'd never feel comfortable giving her back even if I wasn't attached to her. Do I have any legal obligation to give her back? Is there anything I can say to them to prove she is now mine? I'd be devastated to give her up!