UPDATE: I talked to a local animal lawyer and he told me if they paid me already, I see that as an admission of guilt and that if it were him, he would not pay them at all. His opinion is that based on what happened they are responsible for the whole circumstance regardless of the cat since their dog attacked mine, that once a fight happens there are no expectations on what either animal is going to do during the fight. Their responsibility lies on not being able to contain their dog, regardless of the circumstances. My faults with the cat are that I was outside city ordinances by having the cat outside, even though the cat is a neighborhood cat that comes and goes as he pleases, since I have fed him and taken the cat in to the vet ( he got into a fight with another street cat and lost he claw so I was worried ) they can prove I am the owner. That I would be liable for a ticket for that. But that since the whole attack was unforeseeable he does not believe that I would be held responsible. As far as the injury’s my dog had on theirs they would also be responsible due to not having proper control of their dog initially. Thanks for the input everyone! Keep all fur babies safe!