@Melissa-and-Scott0
Melissa, you can't stop specific guests from searching your property and booking it without it affecting their general booking status on Airbnb.
You do say that they were fine, it was the dogs that were not.
I was like you untill I had a couple turn up here with a pair of Burnese Mountain dogs and they did an indescribable amount of damage. So after that.....No Pets, that is my rule. It can be anything from a St Bernard down to a bladder with 4 legs....even though we have a dog, their dog is not welcome here.
You have a permanent message stream open with these guests now I would just send them a message to say........ "In light of recent issues with having pets, we have had to retink your pet friendly status, and in future will not be able to accept bookings that involve travelling pets. Just thought I would give you advance warning of this alteration as it may affect a return booking on your part!"
That should solve your problem for you Melissa without sounding too heavy handed.
Cheers.....Rob