Luckily, you can lookup you fridge model and get the parts list. The part I needed was this:
Also known as a "diffuser". Too bad its almost $90. You might be able to find other places a little bit cheaper, but no much.
If you search on youtube with the part number, you can sometimes get lucky and get a video of some guy replacing the exact same module. This time, I got super lucky, and found a guy who figured out why these diffusers fail, and sold an improved metal replacement part to fix it for far less money.
Removing and opening up my own diffuser revealed that it has suffered the same fate:
Too bad, this guy's in the UK and my food in the fridge wasn't gonna last that long so I needed an alternative. What I ended up doing, was epoxying a bent paperclip around the loop at the bottom and breaking off and filing down the little nubs that were now in the way of the paperclip. I then taped it up (apparently masking tape works well for this) and reinstalled it into the fridge. Time will tell if this hack works.