How to best clean the inlet vent screen on a microhood?
I ended up using degreaser and it worked better than I thought.

First, remove the vent screens.  In a sink, I sprayed liberal amounts of degreaser on both sides and let sit for a couple minutes.  Spray down with water and repeat cleaning if necessary.  Dry on a towel.  Afterwards, they looked like new.

I guess sometimes the simplest approach is best; don't overthink the situation.