Is it right to ask for a refund/not be charged?

If it were me, I would get my cat out of there, not pay a cent and file a complaint against this vet. If he did it to your cat, how many more "mistakes" will he make on other cats?! That is just unacceptable. Your cat will suffer for the rest of his life. I would not let this go. I would be so friggin pissed!!