This a Yom Kippur question. When one bows for Anachnu Korim on Yom Kippur, and the shul has carpeting, does one still need to have a covering between the carpet and ones knees?
In principle, the need for a cover applies only to somebody who is bowing on a stone floor (based on Vayikra 26:1). If the floor is not stone, there is no prohibition involved (see Mishnah Berurah 131:40)
However, the general custom is to place something to cover even when the floor is tiled, and even if it has carpeting.
Note that the covering does not actually need to be under one’s knees, but rather beneath one’s head: Rather than having one’s head touch the floor, the head should touch the covering.