Did you knock and confirm before mowing? Obviously if she calls and says she didn't confirm, there is a conflict of opinion there. You should take this as a learning experience. I don't mow anyone unless I get the okay in person to my face. Calling someone and saying I'm going to mow unless you call to say no isn't a confirmation. What if she didn't get the message? I sent out 3 renewal notices to some people this spring whom I never heard back from, yet I still get calls from those people who didn't renew saying they never got the info or forgot to send it in, etc. I didn't renew anyone who didn't sign the renewal and return it.
If someone showed up and just started mowing my lawn without permission, I'd let them finish too then tell them to hit the road.
Bottom line is, your process is flawed, and in court you haven't a leg to stand. It's called cover your ass, and in the future I suggest you do so. As it is now, you might get paid if she decides to pay you, but you don't have any recourse if she doesn't as far as I can see.