What is the ruling on using a prayer rug left behind (or forgotten) by one of the hotel guests?

Such a prayer rug, which is not usually sought after by ordinary people, is permissible to use and does not require public announcement (ta'reef), based on what Jabir narrated: "The Messenger of Allah, peace and blessings be upon him, permitted us (to pick up) a stick, a whip, a rope, and similar items that a man might pick up and benefit from." The scholars have agreed on the permissibility of taking a small amount and benefiting from it without public announcement. So, if the prayer rug is of the ordinary type that its owner does not usually strive to reclaim, then there is no harm for the hotel staff in using it and offering it to those who need it.