DIAGNOSIS Yes, you can and should wash the outer pre-filter (the nylon mesh sleeve). It's designed for cleaning.
FIX Remove the main filter assembly. Slide the gray nylon pre-filter sleeve off. Rinse it under lukewarm tap water, gently agitating it. Let it air dry COMPLETELY for 24 hours before reinstalling it over the main HEPA filter.
IF THAT DIDN'T WORK If the pre-filter is torn or damaged, you can run the unit without it temporarily, but order a replacement. Never wash the actual main HEPA filter—that ruins it.
HEADS UP Never put the pre-filter in the washing machine or dryer, and never reinstall it while damp. Moisture inside the unit can cause mold and motor damage.