Meaning of Pallet

About a mile from Hume Castle, on the Scotch border, is a rock hill, which is called Hume *Pallet*. The only other name of the kind in this district is Kilpallet, in the heart of the Lammermuir hills, on the borders of Berwickshire and East Lothian. There was at this latter place once a religious house of some kind, and a burying ground, now hardly visible. What is the meaning of the word *Pallet*?