@Tiffany-And-Andrew0
Hi Guys, unfortunately Airbnb are simply a conduit, a go between for guest and host, they put the two in touch with each other but have very little involvement beyond that when it comes to house rules and disputes.
All they will say to the guest if you lodge a complaint is ...."If it's not too much trouble please respect the hosts pets house rule!" and they will leave it up to you as to what action to take.
The guest is obviously catfishing you, the house-rules icon regarding pets is one of the first bits of information on the listing page and people travelling with dogs are acutely aware of landlords pets policy, so it's extremely unlikely they would be responsible for any damage these animals will do, they just expect that as they are there you will buckle under and accept the situation.
I have had the same thing happen here, they almost totally destroyed our garden but all the guest said on leaving was..."I hope the dogs were not too much trouble" and they were gone.
Now I do not accept pets, I do not accept..'I didn't see no pets on your listing', there is a local kennel they can put them into but I won't allow them on the property.
But I am afraid it is up to you to enforce your pets policy, the most Airbnb will do is ask if you want to cancel the stay and it then becomes a host cancellation which you will ultimately be punished for in some way or other!
All the best.
Cheers.........Rob