There are two clips behind the grab handle that slide up to release. If you can't get them to release by lifting up on the door, reach up from below with a narrow stick, and tap the stick with a hammer to push the clips up to release them. When you put the door back together, remove the white plastic thingies (technical term) the clips slide into from the sheet metal, and put them on them clips. When you position the door panel, a couple of slaps in the grab handle area will snap the clips back into place.
You will see what I mean when you get it apart. Just understand there are two clips in the grab handle area, and the panel has to lift up to release them.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)