Try cleaning that area with vinegar and water. My mother swears by it and I've tried it and it seemed to work. The only problem I would be afraid of, is she may find another spot. I have that problem with my Maltese. She does it infront of my diningroom door and downstairs (almost directly below) in front of my laundry room door! Needless to say, I hate walking around with out socks or shoes on, 'cause the floor (especially in the summer w/ humidity) it actually feels sticky. When we got Misty, I pulled out the vinegar and water to clean up after her accidents, and then went and did in the other 2 areas that my maltese was using as her (litter box) and haven't noticed anything in any of those spots. Just yesterday, though, my husband caught my maltese peeing on my runner (that I bought for the little ***, so she will go to the door, since she doesn't like tile floors) and again on my rug (different from in front of the laundry room). When you cover the spot does she still go there? What are you covering it with, paper? Other than that, I'm stumped as well. I know what you mean by damage, too. Good Luck, I'll be checking back to see what other suggestions you get.
Handle every situation like a dog.
If you can't Eat it or Chew it.
Pee on it and Walk Away