I have a door panel in the garage. It looks like you pry the grill out of the ring around it. After you do, the ring that the grill sits in will still be on the door.
Look through the grill with a flashlight - you will see the heads of the four screws that hold the ring on the door. The pointy ends of the screws poke through on the inside; you can't even get the ring off the door without removing the grill first.