Hydrogen peroxide is bleach. I suggest you dilute it, and don't leave it on too long. It is very strong chemical and can weaken fabric. It will bleach out color fabrics and might change the color from one thing to another. I bleached a pair of khaki shorts my husband wore fishing and they gut really gross. threw some bleach in the wash water. They turned orange! I kid you not! And be really careful (ask me how I know!!) if using on batik!
I have never had to remove a burn but had to remove marker.