Are the screws in place? If they are then I would guess that the bracket under the door panel where the handle screws to is loose. If the two screws are in take them out and pull the handle off and you should be able to see if the bracket is loose.
I don't think the handles are available separately from the panel. I would suggest removing one of the door panels and checking to make sure that the two retainers for the screws are secure in the door. I didn't think there were any clips on the handle, just screw holes. If required, the retainers, part number 11570654, are available. Ref. item 15 in this link:
DOOR TRIM/SIDE FRONT | Nalley Buick GMC Brunswick
I'm searching the Service Bulletins, that I have access to, for one that addressed the issue you have. If I remember correctly the instructions said to pop-rivet the bracket back in place. If it was originally tack welded you should be able to see where it attaches.Sorry to bring up an old thread. I just bought an 07 Canyon that the passenger side door has this issue withe the door pull. The screws are there, but the handle moves around. I removed the screws and I could hear the metal bracket fall to the bottom of the door. So it sounds/looks like the metal bracket has broken off. Any suggestions on how to reattach that bracket so that I can get the screw holes to line up correctly and remount the door pull? Thanks!