Carpets were a kind of furnishing found in houses, typically covering the floor.
The Tenth Doctor once remarked that lifts often had carpeted walls, which he was fond of. (PROSE: Sick Building)
Seemingly stranded in 43K2.1, the Tenth Doctor mused that he would have to get a house with carpets. (TV: The Impossible Planet)
Welcoming Ashad and his Cybermen to the ruins of Gallifrey, the Spy Master promised that he would "roll out the red carpet", quipping that it was red because it was "drenched in the blood of [his] people". (TV: The Timeless Children)