@Jan186 the guest will not see your review until the earlier of 14 days (after which it is too late for them to review) or when they post their review. This means you leaving a poor review will not influence their review so please be honest to protect future hosts.
To claim for damage (which will likely fail if they do not agree to pay) you have to do so within the earlier of 14 days or the check in time of the next guest. Sadly the act of claiming is likely to get you a bad review so you have to judge if a claim is worthwhile.
@Jan186 I assume you block day (s) between bookings otherwise your check in and check out times will cause problems. Is the no pets on your listing new? If not you should have turned the current guest away!
@Jan186 You've received valuable insight already, so I have nothing to add except to say, your post reveals that you might need to spend some more time in the Airbnb help pages. Learning for yourself the ins and outs of hosting will make your hosting journey much smoother.
Unfortunately, you have photos of live animals. Many people do not read the entire description and just look at photos. Maybe remove any and all photos of animals in your photos. It states no pets, and you maybe able to contact Airbnb about it.
You can word your review/response for them in a nice way but business like also, pointing out that your rules are not to have pets even though they brought one.
It is always best to leave an honest review so that the rest of us owner's can see it and make that call if we want to host them or not.
