It also helps to guide the cartridge into the cartridge connector. A cartridge slops around without the shield.

Thank you all !

Nope. The noise in a DMG is created inside the semiconductor. A prosound mod is about as good as it gets. In your guitar, the pickups are likely completely passive so they are susceptible to picking up external noise, so the shielding makes more of a difference. Also, the shielding in the Gameboy is more likely to be for keeping things in than keeping them out.

And some trivia, there's actually some copper shielding in a DMG, on the back of the CPU board, soldered to it in 6 points.

Yyyyupp. And due to this fact - with the metal piece You should have better sound on the output (less strange distortions from electromagnetic field).
Also, such a shielding is inside of Amiga or Atari ST. And so on.

^ what he said

I'm pretty sure the shield minimizes capacitively coupled noise from other electrical sources and reduces electromagnetic radiation that may interfere with other devices.

I wonder if putting copper shielding all around the inside of a GB would do anything. I'm guessing that it wouldn't do much but it made a huge difference when I copper shielded the inside of one of my Fender Stratocasters.

Originally, it was put in to act as a shield to conform to electromagnetic interference regulations, as engraved into the plastics on the back of the case. However, since it was designed as an integral part of the case, removing it will leave a big hole in the case where dust can enter much more easily than it could have otherwise.

I want to toss the metal shielding on the back of my clear DMG, is this a good idea? What function does it have?