How to Peel Cooked Beets with a Towel
To remove the skins of cooked beets or potatoes cleanly and easily, simply wrap them in a clean, dry kitchen towel or paper towel, and rub the thin outer skin right off. This is best done while they are still warm from cooking. Be warned that beets will color your towel red, but most of that color will wash out.
Peeling this way removes only the thinnest peel, and thus is less wasteful than a swivel peeler or paring knife.