Oh my GOD this sucked so much. I was trying to mount my 27" thunderbolt to a display arm for a standup desk. It had its own VESA adaptor that required the stand be removed. The instructions showed how to use a credit card to get the stand to show its torx screws, remove them, etc. What it Neglected to say was when you expose those screws you have to really crank down (gently, carefully) on the stand so that it "clicks" in the exposed position.
Otherwise, as you've noticed, the moment you release tension, the mounting bar (The thing inside the machine) snaps back into the display and it is under A LOT of tension. So much you cannot move it without a mechanical aid.
Others suggest you need to take apart the display. That *****, but its probably less physically demanding than this method. But my theory is don't take apart the whole thing if you can avoid it. So here is how I managed to get the mounting stand bracket out of the back of my Thunderbolt display, after I removed the stand and the thing snapped back into the back of the monitor.
1: Get a coat hanger - preferably the coated type so its not metal on metal, and preferably the type with the cardboard bottom that when removed, leaves you with two little hooks, instead of a continuous wire. If you just have a regular coat hanger, you'll need to cut (bend back and forth several times rapidly, don't try to cut) the middle of the flat bottom then create two tiny hooks using a pliers. Also have an allen wrench (with an L curve) handy, any medium sized one will do.
2: Hook the tiny hooks into a couple of the torx holes and make a handle. I did it from the top down. Bottom up might work but I'd worry the hooks would slip off. Wrap a towel or something around the 'handle' or you'll give yourself nerve damage in this next part.
3: With the thunderbolt facedown on a soft but firm surface, ever so gently put a knee on the bottom and on the top (or have a friend hold it down) depress the release bar with a credit card and PULL the hanger. I mean, it hurts. There's got to be 50 + pounds of tension on that **** thing. Obviously be very careful with the monitor edges and where you "push" to counteract all that pull force. Don't actually step on it, dummy.
3a: The allen wrench - if you need a breather (I didn't know it would "click" out when I got it far enough, so I though I had to keep holding it out to put the new adaptor on) I used the allen wrench to get under the spring loaded mounting bar and gentle pry-hold to keep it from snapping back. I also had a bare hanger so my hands were practically being cut in half.
4: So keep pulling hoss! You need to pull the thing PAST where the torx screw holes appear. I can't remember if there was an audible "click" because I was sweating and cursing and grunting so hard, but at a certain point, it locks in the "out" position. Then you can go about your business reattaching the stand or putting on a VESA mount adaptor, or whatever you're doing.
It IS possible to pull out that mounting bracket once it snaps back into the monitor body, without disassembling your (or your work's) monitor. Just do yourself a favor and make sure it is locked in the "OUT" position BEFORE you remove the stand the first time.
P.S. I make no claims about whether this voids or affects warranty, and if you're sloppy and overbearing, whether you won't break your monitor. Be careful and it works. Be aggressive and reap the whirlwind.