Have you ever cleaned them? I tumbled upon this way to clean screens totally by accident.

Have you met Toby? He is our Wheaten Terrier and sometimes ornery. He loves to sneak by me when I am unloading the dryer and snatch the dryer sheet and totally tear it to bits! Sometime ago he had a dryer sheet and was preparing to tear it up, and I happened to be deciding how to clean a patio door screen. I grabbed the dryer sheet from Toby and wiped it across the screen. OMGosh! I looked at the dryer sheet and it was filled with dirt.

Just wipe over the screen. No more trying to take off the screen to wash it or trying to vacuum the screen.

This is a first swipe over the screen.

This is the second swipe over the screen. I usually keep wiping until the dryer sheet has nothing more to clean.