As the cat is still registered in your name legally it's yours. But please can I point out that this lovely little cat isn't a toy. And you have to ask yourself the question. As to why you gave it up in the first place. And for what reason. You may not like the place where it's gone. But constantly moving the cat is just as damaging. At the time of giving up the cat, you obviously thought that the place was okay. And what are you going to do with the cat if you get it back? It takes ages for cats to settle in a new home. So think long and hard before you make a decision. As to where you stand I don't know. Because you willingly gave the cat away. If anything, maybe you should have surrendered it to a rescue center. Who would make sure that the cat is placed in a suitable forever home? You don't say how long it's been. And you need to put the cat's best interest first. If the people are not treating it right then I would contact a local rescue center and ask for their advice.
https://merchurself.com/shop/17th-quarantined-birthday-mug-sick-of-this-shit-2004-mug-17th-quarantined-mug-17th-lockdown-mug-17th-quarantined-over-it-mug/
https://muga-holic.com/shop/i-fucking-love-you-mug-gift-funny-mug-custom-mug-mug-gift-caffeine-best-friend-gift-bff-stocking-stuffer-birthday-gift/
https://pandoraxmas.com/shop/i-know-i-am-not-from-your-sack-dad-sweary-mug-coffee-sweary-mug-adult-coffee-mug-funny-gift-gift-coffee-mug-mom-dad-coffee-mug/
https://dinoxmas.com/shop/i-never-lose-i-either-win-or-i-learn-nelson-mandela-shirt/
https://iteexmas.com/shop/i-tried-to-drown-my-demons-with-alcohol-but-they-can-swim-shirt/
https://merchxmas.com/shop/i-want-to-be-a-nice-sweet-redhead-but-everyone-is-just-so-stupid-shirt/
https://tee-xmas.com/shop/i-wish-i-were-a-cat-so-i-could-scratch-idiots-with-my-claws-shirt/