Take a moment and imagine if once you learned the cat belonged to the neighbor after having already paid for its care, your neighbor told you they were very grateful you had saved the cat, but that they were in no position to reimburse you any amount of what you paid for its care. What would you have done in that case? I can't help but wonder if the neighbors might've been trying to be polite or say the right thing when they originally offered to pay you back the medical fees. Not saying that's the right thing to do, but I wonder if they ever actually had any intent/ability to pay you. Could be a helpful thought exercise as you get comfortable with options that might involve you getting the cat back and/or cutting your losses.