Those aren't typically known as an air filter. They are strainers to allow air to pass without all of the debris, sort of like you are describing. This most likely leads to a plenum area for either an engine air intake or for air being brought into the cabin. A place where you don't want the larger debris getting into.
To clean those up, I think your best bet is to either pick them as clean as you can by hand or use a shop vac and suck the debris off of them. If you pick them clean by hand, you can use a soft bristle brush to pull stuff out of the screening. A shop vac would do a pretty good job of cleaning it out.
In either case, just be gentle with it and you shouldn't have an issue cleaning it out.