My brother and his friend saw some really ugly vandalism done by some very inexperienced idiots at the elementary school by our house. He and his friend decided to paint over it with the matching color to damaged wall. However, they did not ask for permission from the school or anyone; they just did it because they felt it was right. Is this illegal? If so, what can happen to them?

I don't think it is illegal. Where are you, because laws are different in different areas.

However, it is not vandalism, it is removing vandalism, and I've never heard of any laws against that. Even if there were, I doubt the school would press charges, since if they didn't do it, the school would have to PAY to do it, instead of them doing it for free.

Someone else may have the required legal information, but I suggest asking a school administrator about these kinds of things for the future.

PS: I'm glad that your brother and his friend are decent enough to go out of their way to clean something like this up. Not enough good people like that anymore.

Technically they were suppose to have gotten permission from the school as well as most likely the maintenance Union.
I don't know what kind of trouble if any they might be in.

If you don't get permission it's very likely you'll be blamed for vandalism. It looks suspicious.