Is water resulting from washing carpets considered impure if the impurity has no visible color or smell, and what should be done if the exact location of the impurity is unknown?

If you doubt the impurity of a place, do not pay attention to the doubt until you are certain of the existence of the impurity. The carpet you mentioned is pure. Even if it were to become impure, pouring water on it purifies it, and the water with which the impurity was purified is pure. Get rid of obsessive thoughts by ignoring them.