I guess you already figured out it was hopeless to get any sort of compensation as Airbnb refuses to use the security deposit to pay for damages caused by pets.
For your future bookings you might be interested in this special cover that offered to hotels advertising on Airbnb.
By insisting you might be able to get the option if you are not a hotel:
Just had exactly the same experience.
It is despicable to be treated this way when we acted in good faith and secured a security deposit for that purpose.
Apparently hotels that advertise on Airbnb are privileged with an additional option we don’t have as regular hosts.
Here is the explanation from Airbnb UK:
“If you are seeing large numbers of bookings with pets and want to accommodate them, a solution could be that you collect an "offline" deposit for these pet bookings. (Usually it's only for hotels businesses but I'm happy to "enable" your account to do so given the situation described).
Please let me know if that something that could work for you.
Kind regards
Alice
Alice de Saint-Pierre
Market Coordinator UKIE, Airbnb