Welcome to Heartland! Is it the powdery stuff from their wings that left a mess? If you've already tried other cleaners, this probably won't help much, but it's worth a try: brush with a fairly stiff brush to see if any of it is still loose, then try a really good sticky lint roller or some duct tape to remove what's left. If this doesn't help, maybe a weak Woolite solution with a just slightly damp cloth. I have a feeling water will just make the situation worse by smearing it around, so be careful not to get the blinds very wet. (I recently got bright orange pollen on my shirt after a day of flower shopping and learned this lesson the hard way!) The only other thing I can think of is upholstery cleaner, again being very careful to not saturate the blinds. If all else fails, have you thought of stenciling a nice design?
Good Luck!
Update: I just read Walt and Judy's post with the howtocleanstuff link - sounds much more likely to work than my ideas! Let us know how it works.