I just successfully removed, repaired, and reinstalled the "brass tube", and thought I'd share the technique.
As it turns out, the hole in the end of the tube is just about right for a 2/56 tap. Do that (about 1/2" deep), then screw in a 1" cap screw with a nut and a washer already on it. (Or a bigger nut if you can't find the right washer, as in my case...). Then run the nut down, which will pull the tube right out:
Once you're done doing whatever you wanted to do to the tube, put the screw back in and push on that to get it back in place.
In my case, someone had drilled the idle jet out too big. I cleaned up the hole, filled it with solder, and drilled the correct size hole in the solder. Good as new (I hope!!).