@Todd383That is really crappy. I would go back and continue to fight Airbnb on it. I had a situation like that last Christmas, and I fought it and Airbnb ended up refunding the guest out of their pocket rather than mine. In my case, the guest complained about the heating... that they had full control over. I like contacting Airbnb on Twitter @airbnbhelp.
If I can make one small suggestion on your listings, it would be to include a pic of Philip and include a description in the photo title telling guests when, where and how often they can expect to see him. Even though guests have to agree to your terms, so few people read: I think a pic of him might help avoid this kind of situation in the future. I also have three large dogs on site at my listing (same deal, they don't enter the listing), and I have pics up of all three of them.
Your listings are beautiful, and I hope you can get Airbnb to reverse their refund (or pay it themselves).