This is a Kenmore model 106 fridge
The Searsdirect site has a good parts schematic. It looks to me as if two bolts screw into the back of the handle and that the heads of the bolts are fitted into a fixed bracket on the door and the handle slid (pushed) downwards or sideways depending on which door. if it's lose then the trick is to take the handle off and tighten the bolt.
Sears will sell you a new bolt for $2.16 - the number on the diagram is 105 and the part number is WR01X10446
http://www.searspartsdirect.com/partsdirect/part-model/GE-Parts/Refrigerator-Parts/Model-GBS20KBPACC/0432/0161000/G0606263/00001
But I could be wrong...
Peccavi
December 2012