What is this bright white discoloration on the edge of the screen?

This can't be fixed. This is what's called "backlight bleed". I have a Game Boy Advance SP and mine does the same thing.

What model of the GBA SP do you have ags-001 or ags-101? If you are not sure, check the label on the back of the GBA SP and it will be listed in the top left corner. If you have an ags-001, which is the launch model, it is frontlit as opposed to the ags-101 model which is backlit. I have a GBA SP Special Pikachu Edition that I got for my birthday in 2005 and I have never had this problem. I also have an original Gameboy Advance that I modded to have an ags-101 screen and I have never had a problem like that with that system either. The only time I've seen something like that with a GBA SP is with the ags-001 model and that's always going to happen because of the way it is frontlit.

Yes you can fix this. This is the backlight is broken or it is bleeding. You need to replace it in order to fix it. You can find this replacement on this website. So it is possible. You just need the new backlight screen.