The nylon clip is what appears to be broken.
GM part number 9815325, superseded to new part number 16607593.
You can find them aftermarket at nearly any auto parts store. You don't even want to know GM's list price. Sheesh! You can pinch the tip of the piece still in the lock and pop it out, and push the clip off the rod piece if you can reach it. And no, it's not a fun job. If it were in one piece, you'd unclip the piece holding onto the rod length and then you can pull the rod out. Then the clip would be able to pop out of the lock cylinder arm. Simple concept, but as you say, it's sorta tough to work around in there.
They make a LH and a RH clip, but it doesn't matter much here in that the rod clip can be either one and still work. GM truck tailgates use this rod clip too and takes a RH and LH, but the side door lock rod can take either of them.
If you're in no hurry, here's some new GM clips in a pack of 3 for 9 bucks plus any tax. That's 3 bucks each. Not bad.
Find many great new & used options and get the best deals for GENUINE GM 16607593 LOCKING ROD CLIP GM CHEVY DOOR TAILGATE LOT OF 3 at the best online prices at eBay! Free shipping for many products!
www.ebay.com