I would have asked her to pay for the additional people when you realised the guest booked for four but turned up with seven. Or alternatively asked Airbnb to cancel the booking if you as she had broken your house rules but turning up with three additional people.
I hope you left an honest review and raised a request through the additonal guests through the resolution centre.
I would say to her it is clear that there is no communication on Airbnb about her having extra guests and therefore she is mistaken. I would then block her on Airbnb so you receive no further communication.