Found several differing posts on removing the back seat of a 2003 F150 extended cab. After a lot of grunting and swearing, the job is done and I can share it here.
There are 3 brackets along the top of the rear seat back, each side and middle. This pic is what they look after the seat is removed so you can see what the goal is.
And this pic is of the top of the back of the seat, the latch that rests in the bracket.
So you can see, the challenge is to LIFT the seat back up and away from the bracket on the body. I found the easiest way is to hold the top of the seat with one or both hands, either side of the bracket location, and press the side of your knee into the seat back. Lift up on the seat back with both your hands and your knee, giving you enough leverage to raise the latch on the seat up and away from the bracket on the body.
After doing all 3 locations, the seat will just fall forward and release from the complementing/inverse brackets at the bottom of the seat.
Reinstalling the seat is the same process in reverse. Just make sure you get the bottom latches hooked in their brackets, then do the tops.