@Benton1 I'm sorry that happened to you. I would suggest you mention the $15 pet fee you charge and the requirement for guests to let you know if they are bringing a pet when they book, in your listing description, not just in the house rules section, because lots of guests don't even bother to scroll down to the bottom of the listing page to read the house rules.
But I don't quite understand- this guest got refunded because you asked him for the pet fee? Did you not have it in your house rules when he booked?
You might be able to get that review removed. Contact Airbnb and ask them to remove it based on irrelevancy- he doesn't explain what wasn't as advertised and if it was because you asked him to pay the pet fee and you had that requirement listed, it is definitely irrelevant.
If Airbnb won't remove it, then yes, you should delete the listing and start over with it. You'll never recover from that 1* rating, and it will keep people from booking.