Handbook of ROCOR Liturgical Practice:

Who can or should place and move the eagle rugs (orletsi) during a Hierarchical Service?

The movement and placement of the eagle rugs belongs by right to the Subdeacons, or in their absence to the other Altar servers. Deacons, Priests and Bishops themselves should never touch these rugs, out of respect for the purity of the Lamb that is held in their hands; but in all cases, it is absolutely forbidden for a Priest or Deacon to move an eagle rug after he has washed his hands as part of his vesting, or otherwise put on his vestments (if a lesser Divine Service) — since the eagle rugs are, after all, rugs, and lie on the ground and are stood upon, and therefore become dirty; and the washed hands of the Priest and Deacon must be kept clean for the ministration of the Holy Myteries, as well as touching their sacred vestments.

Should a Deacon or Priest by some extraordinary necessity handle an eagle rug after washing his hands or donning vestments, he must immediately go and wash his hands again before he does anything else.