@Kia272 Cats love climbing through curtains and jumping up onto sunny windowsills. They love playing Curtain Monster. Cat owners know this very well. So unless you've somehow cat-proofed your curtains, I think you're being suspicious for the wrong reason. As a guest, I would certainly not leave curtains open if I had any inkling that I had a nosy host who might come around trying to peek into the house...which, and I mean no offense by this, sounds super creepy.
The genuinely suspicious detail is that the guest waited until the day of the booking to ask about bringing the cat. Any responsible pet owner would make the effort to seek out Pets Allowed listings, or at least ask in an Inquiry before booking. In this case, the timing means the guest was probably not asking for permission but rather pre-emptive forgiveness; he probably had every intention of bringing the cat anyway.
As far as your concerns about pets and allergies go...well, if there is a cat in the house, the damage is already done, so it doesn't seem like confirming it now rather than on the checkout date does you much good. But if it's eating you up inside and you really want to get in there, just make up a pretext for it (like a meter that needs to be checked, or an item left behind by a previous guest that you need to retrieve) and announce via Airbnb messenger that you'll be arriving at xx:00. While a couple hours' notice would give them a chance to exit the property or sneak their cat out into the car, it probably wouldn't be enough time to remove every trace of fur or litter...and your allergy might double as a sixth sense.
If you take this course of action, you should have a plan in mind about how you'd deal with discovering evidence of a pet. Will you terminate the booking? Attempt to charge an extra fee (knowing that Airbnb won't necessarily enforce it)?
