That's one of the scary moments. Are you sure you have all of the screws out? IIRC there are three screws on the lower metal bracket (holding the bottom of the glove box), one under each of those plastic cover tabs and two by the hinge/bar that the door latches to. If you have all of those out you still have to give it a bit of tug. It will wiggle a bit but feel like it doesn't want to come out. I was sure I was going to destroy some delicate trim piece as I was yanking it out.
A monkey could change the filter in my Sienna with no tools in 5 mins. Squeeze hinges together, drop glove box door, open filter lid, swap filter.