How to remove this board to board connector? (Home Theater Amp)
That is a 2-piece connector. The top piece has an ear at each end which is held in place by the sort-of-triangular bump you see in the cutout in each ear. What you need to do is take a very fine screwdriver or knife blade at each end, and bend the bottom of the ears out unit the bump disengages. Then you can pull the top piece off straight up. Now you'll find that each wire is held in place by a pair of vertical prongs which stick up from the lower piece. The prongs pierce the insulation and grab around the conductor. (this is why it's call an IDC, insulation displacement connector). You'll need to pull each wire up to free it from the prongs, being careful not to actually bend the prongs. 

After you've ruined a connector or two, you'll find it's pretty easy.

And reinstalling the wires is fairly straightforward, but not necessarily convenient. Cut back the wire until you have smooth cable. Place the end of the cable on top of the prongs. Put the upper piece in place and squeeze the upper piece down, forcing the wire onto the prongs, until you hear the ears click into place. Be aware that this is usually done with a special tool. If you make a spacer to put under the board with cutouts for any connections (such as, specifically, the connector pins) you may be able to do it in a vise.