I say, with Allah's guidance: If the impurity on the carpet is visible and has substance, it is purified by removing its visible part. However, if it is not visible and has no substance, like urine, it is purified if the carpet is placed in running water, or if a large amount of water is poured over it and flows over it for a day or a night. It is purified without squeezing or washing three times, because it is not possible to squeeze the carpet, and with the flowing of water, it is assumed that the impurity is removed from it. The estimation of a night is to eliminate doubts. See: Al-Wiqaya p. 131, and Fath Bab Al-Inayah 1: 245, and Allah knows best.