The button is held in place by a beam and its corresponding slot, which is why it cannot be lifted straight up.

Take out the 2 screws for the left button and remove it in the same way as the right button. The screws for these two buttons are the same.

Putting the buttons back on is fairly straightforward. Just press down while pulling it backwards, the opposite motion of taking them off, and they should snap into place. Make sure to put the right button on first.