I can't re-attach my thunderbolt display stand
I just experienced this and I had a heck of a time finding anything online about it, so I thought I would answer.

The flange probably isn't properly stuck, it's just very, very highly tensioned. I threaded two relatively thick pieces of twine through two of the torx screw holes. I then actuated the release mechanism and pulled really hard on the twine. Like, really hard, harder than you probably imagine it should need. The twine broke when I only had one piece threaded.

This should be sufficient. Once you get it out, it should lock back in place and you can continue as normal