As with most electronics, its screens are especially vulnerable.
It’s possible some scratches may appear over time, especially on the bottom touch screen.
These pastes can permanently damage touch screens and turn a simple scratch into a disaster.

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Use a soft microfiber cloth designed for electronics or glasses.
Dampen the cloth with water only.
Don’t get the 3DS wet and don’t pour water directly on the screens.

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Wipe off the touch screen and the upper screen.
Rub the scratches for several seconds.
Use a dry part of the microfiber cloth to dry the screens thoroughly.

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Dab any dust or smudges with a piece of transparent tape.
Repeat the wiping and drying with the microfiber cloth if needed.
Nintendo suggests an upgrade or replacement for 3DS units that are badly scratched.

Lifewire / Nadia Oxford
Scratch Prevention Tips
Here are a few tips to keep your screens blemish-free: