I've done three over the years, and never found a reliable method. I just soaked them and futzed with them, cussing creatively, until they came out.
IIRC, it just pulls straight down, but twisting and lots of solvent over time will help. It's also _possible_ that just soaking the screen in solvent in place and blowing compressed air back into the muffler will clean it enough (never tried that). Another possibility, start the generator (after using only non-flammable solvent, please :)) and let it run for a few minutes, in the hope that differential thermal expansion will break it loose.
Jim, "I've taken a vow of poverty. To annoy me, send cash."