I don't use any manipulating cloth with my TBHs. What I do have is a strip of cardboard about the width of two and a half topbars and slightly longer than their length. In the centre running along the length is a small piece of wood glued on to use as a hold and to prevent them flopping around (Old rocket sticks are ideal.. and free) . When I have removed a topbar, I place the card over the vacated space to prevent bees exiting. When it gets soiled replace it with another. Easy to carry and costs nothing. I keep one under each hive top so no cross contamination and no carrying them around..

The lazy man's guide to doing the minimum possible.