I would try washing the band. It turns out the human body, in cases of heat or activity, can excrete a watery-like substance from the skin. This substance contains water, oils, salt, and sometimes even dirt! In addition, when the 'water' evaporates (a complicated process by which the liquid turns into vapor - amazing!) it leaves the residue materials (salt, oils, etc.) behind, which can often appear white.
Moreover, you'll find that skin cremes, or especially insect repellant or sunscreen, leave markings behind on 'rubber' materials. These can stain and are often impossible to remove because they literally react with the band's materials.
Post pictures POST washing and/or let us know what other than water/skin was in contact with that band.