patty, they came into your yard without letting you know. if you had always put the dogs in before, when they were there, i can't see how it could be your fault.

don't give this man any money. it will cost him more to sue you than you would have to give him in court.

ignore him. end the association with them and cut your own grass or whatever it is that he's doing for you..........xoxoxo pat

p.s. write a nice letter, NEVER mentioning the dog and injury, and tell them you've made other plans for your backyard. that's all. keep a copy of the letter......
today, write down every word of your conversation with him. particularly that he told you that the deductible has been met and what he said about ER.....