@Trond26. Hi Trond. Your place your rules.
I have learnt (the hard way) to slip some of my rules early into the description to set expectations. For example I say something like pets are welcome but not on beds please. Then I provide a throw over the couch, a dog bed, dog blankets and dog towels. the showers are walk in with hand held roses so you can actually wash the dog in them; assuming you dont want to use the outdoor shower. The beds have a mattress encasement (bed bugs), then a waterproof mattress protector, then either a cotton mattress protector or topper.
But getting back to your question of what to do. If they broke your House Rules (and you can clearly show the rules and damage then submit a claim with Airbnb. Do not submit claim until they have done their review, or at the last minute. By contacting them about it you have placed them in a defensive position. Obviously you didnt do the damage so just document it all.
Try to weigh up whether the damage is worth claiming. For example I had a family stay and clearly one child had an accident. I was able to strip the waterproof cover off and no damage underneath. A good warm wash, some sunshine and its sorted. My topper just came back from the dry cleaners. $A45. That was more about sweat than anything else.
Re scratching I'd put that down to wear and tear unless something is actually broken and yes I ask that dogs not be left alone too. As a result I have let go a few bookings. I tell them most of our guests come with a dog to be with that dog, not to leave them as thats a kennel. Here its no excuse as its dog heaven with friendly and understanding eating venues, off leash parks and 6.5 miles of off leash beach.
Put yourself in your guests shoes and prepare for the furry ones as best you can. Hope this helps.