You have the right to know the procedures you are paying for. What is to keep them from having all sorts of things done to their dog on your dime if you don’t know what is being done. It’s not like you are asking for the dogs health records. The owners need to work with you since you are taking responsibility. If this turns into an issue, you can call Legal Aid. They will just give you some advice at little or no charge, and a course to follow. This will show you are trying to be responsible for your dogs behavior, but the owners are refusing to allow you to know what you are paying for. I wouldn’t pay for anything until I was handed an itemized bill. So until the owners contact you, I wouldn’t shell out a dime, but I would consult legal advice for my own protection.