If they can be removed from the window frame, then you have a number of options. My best suggestion is to set them up against a fence or something where you won't mind what the removed pollen will stick to. Then, start by using a plain, old, dry paint brush at least 2" wide, and start dusting! Do both sides and keep your eye on which direction the wind is blowing. You could easily be doing double-work as a result of working upwind instead of downwind. You'll need to dust BOTH sides so flip them around. After that, get yourself a bucket of warm water mixed with a very little amount of Joy or Palmolive or something. You don't want to make a lot of suds so be sparing with how much you put in the bucket. Then, take the same brush and 'wash' the screens, both sides.
IF the screens are NOT removable from the window frame, close the windows first and do a dry dusting with the brush on the OUTSIDE screen first. Then, go inside and clean up what you can BEFORE you dust the inside of the screen. You have to be conscious of the wind blowing into the house. So, close the bedroom door, or whatever doors or windows are in the room and do one at a time. My best to ya and hope this helps.