Charging for a dog bite?

A 10lb, 14 year old Lhasa Apso just bit me on the thumb while I was trying to crate it after its 7th accident in my house today—it got dropped off this morning.

Before agreeing to book, I made it clear that the first 4 accidents are free, but after that, it’s $10 per accident on the floor and $30 if it’s on furniture. I wrote this up in my notes on Rover after our meeting.

I’ve been updating the owners with every accident and sent them pics of the bite. After crating the dog to let it calm down, I waited until we reestablished trust before taking it out for a walk.

I called my doctor, started antibiotics, and got a tetanus booster. The owner says its rabies vaccines are up to date, but I’m going to ask for proof when they return.

How would you handle this? Any other advice? Is it fair to charge for the bite?

Appreciate your thoughts!

Edit:The main reason I came upon with this rule of charging after the first four accidents was the blatant lying I experienced during the holiday season. A few owners claimed their dogs never had accidents, which was not true. I must have cleaned up 20 accidents, despite putting diapers on then and putting down training pads.

I feel like 4 accidents is enough to separate those who are just anxious in a new environment from those who are not house trained. If the owners feel confident that their dogs are house trained, this isn't an charge that should effect them.

Can you help me to understand why this is unreasonable?

Edit 2: I was told these dogs were house trained before booking. The owner then dropped them off with pee pads last minute.