Don't let your clean windows be overshadowed, if it needs to be done get it done. You can ask me when I arrive what I think and I'll give you an honest assessment.
To remove the screen, apply soap and water, give it a scrub, dry it, and reinstall it.
What good is it to have freshly cleaned and sparkling windows if you're just going to put filthy screens over them? Years of pollen, dust, and dirt from new construction can get trapped in your screens making them even dirtier than your windows! Well, you're in luck! I clean those too. Now, they don't always need to be cleaned. Depending on the location of your house, age of the windows, and surrounding activity this isn't always necessary. If there is just a lite dusting with maybe a little cottonwood fluff, I routinely just brush that off, but if they're dirty they need to come off to be scrubbed and dried. Sometimes the homeowner does this while I'm washing the windows, but if you'd rather not I don't blame you. It really is dirty work. It does take me some extra time and is priced as follows: