As someone who recently went through this exact scenario, let me say: you will not be pleased with the outcome.
I do not allow guests to bring pets. I also charge a $400 security deposit. Before COVID, I had a guest sneak a dog into my home for a 4 night stay. It urinated all over my laminate flooring, shed everywhere and chewed part of my front door. The guest literally left urine on the floor, she didn't even wipe it up. It soaked into the floors & bubbled as a result. My cleaners took photos: hair everywhere, dog food in a dish on the floor, urine puddles, you name it.
I filed a claim immediately with the guest - surprise! She didn't answer. After the 72 hour period, I escalated it to AirBNB. I was immediately told that pet damage is not covered by the Host Protection Guarantee, even if your listing states 'NO PETS'. I escalated the claim to their arbitration department, saying if they wouldn't cover me from the Host Guarantee, then they should deduct the amount requested from her security deposit. The CS rep stated he'd 'reach out to the guest' for her side of things. A week went by, and the rep reached out to say that the guest was requesting the photos I had submitted with my claim. I allowed him to send them to her (despite her having been sent them already but I digress). Another week passed. Finally the CS rep reached out to me and said that 'the guest is no longer responding to my correspondence, so I cannot release the funds to you without her approval.'
What a complete joke. What's the point of arbitration/mediation when all the guest has to do is either refuse to pay, or disappear entirely? Guests can bring pets into my 'No Pets' home, damage my property and I have literally zero recourse. The only thing the rep mentioned was that it would have 'helped my case' if I had specifically mentioned in my House Rules something to the effect of 'Guests who bring pets into my home will be subject to a $XX penalty.' Because you know, it should be on hosts to imagine the million different ways guests could potentially break your rules and then set specific 'fines' for each in your house rules like a deranged person. Can you imagine a guest looking to book your home, and seeing a list of 20+ 'fines' for infractions?! They'd run for the hills. Anyway, I got $0 for the experience and my guest (who had 4 5 star reviews, by the way) is free to do as she pleases. The only good takeaway was the incredibly detailed, scathing review I left her.
I am very much looking forward to switching to long-term rentals once COVID has passed. That experience left me absolutely disgusted. All the best to you!