With the clips removed, these plastic tubes, which keep the armrest from wiggling, should be able to be pried out.
There’s a button in front of the armrest. Press it to flip it up.
This will give you access to the inside bottom portion. Pry back here gently…
…and the armrest should finally be released. The part you see here will stay on the car. To be honest, after having owned this car for two years, this was the first time I ever realized I could put anything inside the armrest, having never noticed the button at the front to open it.
This is to show you the orientation of how that spring clip goes, and to show you we’re competent enough to put it back on (because it was a pain and I had my doubts of any success here).