First: take a deep breath. It's not that bad. I recently installed the VESA adapter for the first time and did not get the latch to properly lock in place. After removing the eight Torx screws from the stand, the flange buried itself back into the iMac. A credit card will not work to get it out. It requires some wire and a strong arm - an extra pair of hands are helpful. The steps are:
1) Patiently thread wire through each of the eight holes. Picture hanging wire is probably the best option if you have it. I did not have it, and did not have the patience to go buy some, so I sacrified an old ethernet cable. If you do the same, just remove the rubber/plastic casing from the ethernet cable and extract the eight wires inside.
Note: there are other posts online that suggest using fishing line, thread, or floss. I tried thread and floss multiple times with no success. Also, do not try to snag wire around the pin on the flange and pull it out - the thread or floss will most likely slide off of the pin.
2) Twist the wires together and around a handle of some type (a screwdriver works, but don't stab yourself or the iMac with it as you pull).
3) Pull straight out (hard) on the wires. When the flange reaches is "normal" limit, use a credit card to release the latch that allows the flange to come out of the iMac.
4) Pull straight and down on the wires until the flange locks in place.
5) Have a drink.
Also, let this post be my statement of dissatisfaction regarding the design. It is tricky getting the flange to lock in place and the flange takes a lot of force to pull out. There has to be some design changes that would make adding the VESA adapter less risky.