What is the ruling on praying on a prayer rug that has been exposed to leaked rainwater mixed with cat feces and dirt, and has been cleaned by drying or with a wet towel?

Cat waste is impure, but the default state of water and other things is purity, and it does not become impure by doubt. Rainwater is pure, and its passing over cat waste is merely a possibility that does not render it impure. The change in the water's color might be due to dirt and dust. The default state of substances and water is purity, and there is no dislike in asking about the purity of water flowing from a spout unless there is evidence indicating impurity. Based on this, prayer on the aforementioned carpet is valid because it is deemed pure.