This is probably from moisture - it lifts the fibers similar to raising wood grain. It's like a lot of hairs standing up on end. If you've wet the wrap to clean it or sweated a lot, it will get this way.
There's a couple of things you can do quite easily. What I would recommend is to sand it lightly with 1500 to 2000 grit paper turning the cue in the direction of the wrap. You can mask off above and below the wrap to be safe. Sandpapers of these supe-fine grits can't damage the wrap.
Then take a piece of Parchment Paper which is a silicone impregnated paper (from the cooking section where aluminum foil is in the store) and agressively rub the wrap by holding the forearm with one hand, gripping the wrap with parchment paper, and moving is back and forth untuil the paper gets hot.
The sandpaper removes the fibers, the silicone in the parchment paper burnishes and seals the linen. You can also use wax paper, which gives the wrap a very slick feel. I prefer parchment paper myself.
Chris