Actually, I have try. The result is not really good. But I think I can make it better next time.
First, I use diluted thinner (about 1:2) to wash out the painting. Be careful, the thinner will melt the plastic. I did once before.
Just wash the parts with painting. Dont touch the middle part.
Then, I use tamiya X20 thinner to wash the remaining painting. I am not sure if X20 can totally wash the painting. I will make a try.
After that, I try to brush it with Water Mill sandpaper (2000), but I don't recommand. I am not sure use 5000 Water Mill sandpaper will better.
Lastly, use metal polish to make it.
If fact, the old gameboy won't have a shinny plate as well.

Of course cutting a new plate is the best way, but i would like to keep as much as the original parts in it. I will try again.