At home I tried this trick, and so I now own 2 Casio calculators with a reversed display. The modification took about 5 minutes. But what is the secret behind...

The fact that you can simply turn a normal display into a reversed display  meant that the twist of light of the LCD of the calculator should be about 45° from the display's baseline, because then the polarized grid on the protection screen should also be 45°. If you turned over the screen, the polarization should be (180-45) 135°, so that what is normal reflected by the green background will be black, and the black digits become transparent, so the background will be reflected through them. If the polarization was 90° from the baseline, it would not have any effect on turning the polarization filter, because it would stay 90° after turning around.

This meant that the fascinating reversed displays on a G-Shock is not a very difficult thing to make.  They just put in a polarization filter that has a 90° twist of that of a normal LCD display.