The thumb cap hides a small bracket that holds it on. It pops into place if you push the bracket and cap together quickly. I had to take the inside door panel off in order to finess it back on. You can pop off a rubber cap in the door jamb and peek in there.
On second thought, that small bracket might not be responsible for holding the actual handle in place, just the plastic thumb cap, so you will probably need to remove the interior door panel in order to access the bolt or nut holding the handle on.
Tape up the area so you dont scratch paint.