Are these throw rugs you're talking about. Reason I ask is some years pack my dogs would do the same thing, pee on the rug I had in front of the kitchen sink. I thought they were getting confused with their pee paper and the rug, what the heck, something laying on the floor, lets pee on it, they also did not poop on it. I removed the rug. Those girls are now passed. I agree with what Belamia has suggested. When my girls were doing this I ordered on line ZERO ODOR.web site
Zero Odor Pet | Zero Odor I would spray the rug, let it set for several hours then wash the rug. They would pee in diff. places on the rug so I just gave up and removed the rug. Good luck it can be frustrating.