You can pick up the hair, add the straw, and put the fur back on top. I have had some does use the box as a litter box. They did it up until they kindled in it, and then stopped. I put cardboard in the bottom to help cover the floor of the box, and clean the box out every day until she kindles. It can be an annoying issue. One of the does only did it before her first litter, and not with subsequent litters. When it is warmer out, I will put in a wire nest box with some straw in it and no cardboard liner so the urine goes though it. Then I clean it and line it with cardboard once the kits arrive. I wish there was an easier way to get them to stop!
You can also make sure the nest box is not in their potty corner, but they will sometimes do it even if it isn't.