Hi Cranberry,
The part your looking for is #8201537. You can see it
here.
Threading it through the door is simple if you know the secret to it. First you need to go to hardware store and get something
like this about an inch, inch and a quarter. Take a piece of 1/4" tubing with you to make sure the "all-thread" will screw into the tubing snugly.
Now, screw the all-thread into the spout end of the existing tubing (the one in your fridge right now) about half the length of the all-thread. Then take the tail end of the new tubing and thread it onto the left over stub of all-thread.
Open both doors and remove the bottom grill (it's snapped in place) then close the doors. Below the freezer door hinge, you'll see the tubing coupling. Disconnect it and remove the ferrule for use on your new tubing later. Now at the same time, begin pushing the tubing from the top and pulling it from the bottom.
SG