Cat Adoption Agency Is Attempting To Re-possess My Cat

I feel like I'm in an episode of Air Bud or some Disney film where the evil corporation is trying to steal my fucking cat.

Rewind 3+ months. My friend T gave me a kitten. Kitten and I have become best friends.

T and adoption clinic had a falling out. She lets slip that she gave the cat to me. They are now pursuing the return of the cat, according to the clause in the contract she signed

“I understand that if I no longer want or am no longer able to care for my adopted pet, I will surrender my pet to "petty emo girls" and provide transport to where "middle-school drama creators" deems appropriate."

Mind you, I did not sign this contract, nor would I ever sign a contract for a $50 adopted pet.

This is not about the money to me, I just don't want any kind of ongoing legal obligation big or small to people that behave as they have in the course of the past month or so. Awful, scathing emails devoid of any empathy or human connection.

They are operating under the guise of "doing what's right for the animal."

This is not the case, as in the one email that I sent to them, I explained that given that the kitty has been in my care for 3+ months, she has adjusted wonderfully we have a stellar relationship, and even provided receipts for the goods & services I have bought for said creature.

Nowhere in this contract that T signed, is there any explicit statement of ownership of the animal. Only that one clause which is pretty weak, imo.

So, the way I see it, this cat is mine. I have been caring for her, and she's honestly my closest friend these winter days.

They are threatening to take us to court, which I assume would be small claims?

If the judge were to see this, I'd hope that they would understand both sides of the case, and make a humane decision.

At this point, I'm really just trying to operate according to my values, which includes not signing a lease for a cat, and also not folding and returning this animal that I have developed a sincerely beautiful relationship with.

Does anyone have any thoughts on this matter?

It seems the Internet has examples of both sorts of outcomes in situations like this, but this is usually over pedigree animals worth thousands of dollars. Obviously emotional connection and abstinence of unsavoury legally binding documents is my goal here.

Edit 1: state is pa