Providing a full refund for stay?

I had a dog stay with me that had never been away from home and the dog was not socialized and people spooked him. I met him beforehand as they suggest and he seemed fine with me. I normally have pet gates up in my home so that dogs can't escape out of my front door. The dog was nervous on bare floors (I have tile and vinyl planking on my first floor), which I was aware of, however, the owner did not inform me that he had any issue with pet gates. Also the owner has bare floors as well so it's not that he couldn't walk on them at all.

He wasn't dropped off by his owners, instead a different person dropped him off and they didn't say he didn't know how to use a pet gate and he went through it a couple of times while this person was there with no issue. (It's the kind that has a door within in so you don't take it up and down) Once this person left and I opened the gate to go lock the door, the 125 pound German Shepherd ran through the gate catching his leg on the rails due to being nervous and upset at being left, he pretty much pushed me out of the way to do this otherwise I would have tried to stop him. His leg was a bit cut up from this and so I dressed the cuts and the owners did not tell me to take him to the vet when I informed them. They were aware that he was walking fine, no limp and I monitored the cuts the make sure they were healing--which they were. He was eating, drinking, walking on a leash on concrete, including steps just fine. And when they picked him up he was running around with them and got into their car just fine as well. Now they're telling me they want a full refund. Should I provide the refund? I feel bad but I feel like I should have been informed that he couldn't handle a gate but it was also for safety purposes, especially considering that he wasn't trained, socialized or super great with people. I also tried to make the floors as easy on him as possible by putting down towels and sheets so he felt better about walking on them.

Also--do you use pet gates in your house? Did I make a mistake by using them? None of the other dogs I've watched have had an issue with this. Thanks!