The US Governement issued one complete wash kit to each soldier. In this kit a towel was of course provided. Early war, towels were white but from mid-War they will be Olive green for camouflage purposes. 
This towel is not made of a traditional terry towelling material, but rather an interwoven cotton fabric that is far coarser and much worse at absorbing water.
This example is a mid war type with maker or initials stamped, W H or H M ? 
A nice piece in nearly mint condition. Only one for sale ...