My dog was opened to confirm spay. Should vet have known? Do I pay?

It is not always possible to know if a female dog has been spayed simply by examining them. Some spay scars are very small and cannot always be seen or felt. It is also possible that scars from incisions may have been from other surgical procedures, such as foreign body surgeries, c-sections, or bladder stone removal. The only surefire way of knowing if a dog is spayed is to perform a surgical exploratory to actually looking for the ovaries and uterus, or have an ultrasound performed by a boarded veterinary radiologist (although this often costs more than a spay surgery). I suggest discussing this further with the vet who performed Annabel's surgery if you have additional questions, but it sounds as though everything done was medically appropriate.

As a side note, I can see in the picture that Annabel's incision is a bit red. Just be sure to keep an e-collar (cone) on her at all times for the next 10-14 days until her incision is fully healed. If she licks at the incision, it is likely to become infected and may even open. I hope that her recovery goes well!