Is it sufficient to remove the عين النجاسة (physical impurity) with a damp cloth and rub the spot, or is it necessary to pour water on the mattress or carpet to purify it?

Purifying a mattress, clothes, or a rug is done by pouring water over the spot of impurity until the water separates without its color or smell being changed by the impurity. A strong presumption that the impurity itself has been removed is sufficient; certainty is not required. Therefore, purification is not achieved by wiping the impurity with a water-soaked tissue, but rather by pouring water over it.