DIAGNOSIS The two charcoal grease filters at the bottom of the vent hood get caked with grease over time and can seem glued in place. They're designed to slide out toward you, but the tracks get gunked up.
FIX 1) Put a drop cloth or old towels on your range below. 2) Use a putty knife or a thin, stiff piece of plastic. Slide it carefully into the gap between the filter and the microwave body to gently break the grease seal. 3) Once you can get a grip, pull the filter straight down and out. Don't twist or yank it sideways. 4) Soak it in hot, soapy water (Dawn dish soap works great) or run it through the dishwasher. Let it dry completely before sliding it back in.
IF THAT DIDN'T WORK If it's really welded in there, you might need to remove the lower vent cover (sometimes called the grease duct) itself. There are usually a couple of screws inside the cavity holding it. Removing the whole panel gives you better access to push the filter out from above.
HEADS UP These filters are not meant to be replaced with permanent ones. The microwave's venting performance depends on them being clean. If they're damaged during removal, you need to get the proper GE replacement filters for your model to maintain airflow and fire safety.