Once in a while I wash a load of clothes not knowing that there was a kleenex in a pocket. When I take the load out, there are fragments of kleenex stuck to the clothes.

The solution is to put the clothes in the dryer with a Bounce softener sheet. The kleenex pieces are stripped right off and wind up in the lint trap.

Perhaps you could put the blanket in the dryer with a damp towel and a Bounce sheet and the white lint would wind up in the lint trap, like the kleenex.

Don't use high heat, and don't forget the damp towel.