Blowing the deceased insecta
species back the way they came is vastly easier than blowing them through the screen that caught them, so you will want to work
from below. If you have compressed air, this is the time to use it. Using water
from below is likely to be messy. But then, those screens are advertised as easy to mount, so they should be easy to dismount and wash.
Which way does your air flow? If you can arrange to exhaust
rather than suck into the cabin
, fewer bugs will sacrifice themselves on the screens.