TL:DR

The cat I've been taking care of for the past months, the owner has now appeared out of nowhere claiming that the cat is hers and I'm stealing her cat . The owner claims the cat is an outdoor one, however it doesn't have a collar, was in scrawny condition when I met him, also had fleas and worms when I took him to the vet, meaning he wasn't taken care of. In addition the registered owners of the cat were contacted several times by the vet and they never responded. This woman is threatening to take me to court over this.

Since the pandemic started in January and a bit earlier there has been a cat which walks by my backyard and general home area, after some nights of observing him, I decided to give him some food (the cat didn't have a collar or anything and always have branches or burs in its fur), and give it a place to sleep in my backyard. I made a little catbox so he could sleep inside it and be protected from the elements. After some months of this the cat eventually grew accustomed to me and even friendly (he'd follow us anywhere in the backyard area). At this point I didn't know who's cat this was so I wanted to check if anyone posted about a missing cat, I then took him to the vet to get him checked for a microchip (which he had but the previous owners had moved apparently and left the cat). After contacting the previous owners, and with no reply. I decided to start treating him like my own cat, by letting him into the house and sleepover whenever he wanted (he'd only want inside at night or when the weather was bad, otherwise he'd be out and about). Almost 2 months later, still actively searching for the actual owners of the cat, we find out that some children are the owners of him, but they said that he doesn't get along with their own house cat so they let him outside instead and they only see him in the mornings. After this encounter things seemed fine however, maybe 2 weeks later I get a call from an angry mother telling me that her children are worried about where their cat is, and also that she will go to court if we don't release her cat (we didn't have the cat at the time, he must've just been roaming around). Anyways she speaks in a very aggressive tone and threatens to go to court over this cat, and states how we "thefted her cat", when in fact I just give the cat food and shelter, what's more, is I said she should take better care of her pet because it was clearly negligent behaviour to be leaving your pet out at night in storms and any other weather events that occurred during the past year, to which she just ignored and stated it's not my business, and I should stay uninvolved. However this cat was without a collar scrawny and always scrappy when I found him, and when I took him the vet, they found a number of issues with him (worms, and fleas) which were left untreated (clearly the mother didn't care for this cat). She then went on to say that she is a lawyer and would have no issue going to court (basically just trying to drill in the fact that she can go to court). Also after receiving the call from the angry mother I decided to call the vet, to confirm that the mother was the owner of the cat, to which the doctors laughed and said that they hadn't been able to contact the owners of the cat after multiple attempts. I'm unsure of what to do, if I should just ignore her calls and claims, or if I should try to fight back and go after her for claiming this cat as her own when she has been a negligent pet owner (would that work out?)

also, I'm pretty mad about the fact that her go-to move was to bring it to court, I feel like that is an abuse of power for a lawyer, especially for such a small issue like this.