Insurance companys do not pay out just because someone makes a claim.
They will fight your corner for you and refuse to pay.
Let her fight it out with the insurance company 
Be careful with this one. We did exactly that on the domestic cleaning side for a claim we were sure they would not pay as it was not cleaners fault. They did - paid £2000 directly to the complainant without advising us.
On top of all the advice here, any chance the customer has moved furniture and laid, for instance, oily castors on the carpet, and is now trying to get you to pay for her mistake? Is there a pattern?
Does sound like wicking up of some sort though.
If the marks won't go, your strongest defence will be the fact that they were not there when you left and the fact that she has made the marks permanent. Be adamant about this.