Are you spot cleaning? or the entire piece?
Dry cleaning is a joke, so I never offer it. Master blend has a dry cleaner, almost every manufacturer has one. Spray and towel. Still have to watch out for a soil ring, Feather it.
As per wet cleaning:
Depends on if the cotton is refined or has some remnants of the seed of the cotton. Test on a zipper side with what you're cleaning with for browning or brown specs.
PC has a delicate fabric pre-spray and a delicate fabric detergent. Or follow with a mild rinsing agent. If browns or specs use the white cotton formulas, though you'd wnat to test how the linen does with it. If using it, I'd go with a diluted one (not as strong as suggested as it is too strong.)
If it does not work, send the bill to Richard. He'll take care of you.