I have never seen white scrim for sale. In olden days when chamoise and scrim was all we had you would be washing your scrim several times a day in clean water, no soap. Mind you in those days soap powder wasn't what it is today either. The only time that scrim was washed in detergent was for the first wash, my bosses mrs used to hand wash them in Dreft after they had been boiled. The scrim never saw soap again. With the constant washing the srim became whiter, an old one would be nearly white.
Now to get back to dusty scrims, A new scim will allways fluff up as we used to call it when it became dry. We never used dry scrim, it was always damp.
I don't know if it's because we have very low TDS tap water, but, after we chamoised the glass we used the damp scrim, this would leave a thin film of water on the glass but it dried perfectly clean.
I use dry scim now for detailing, but when polishing leads or other handwork, DAMP EVERY TIME. use one of those plastic spray guns with unsoaped water to dampen them. Make a pad out of your scrim and keep changing the part that is in contact with the glass. this keeps it clean longer. Dai