That looks like mold or some sort of mycelium.
If it is mold, hydrogen peroxide might not do much:
"The beauty of peroxide is that it does not kill established mushroom mycelium or interfere with its growth and fruiting.
Despite peroxide’s wide range of action against the common contaminants of mushroom culture, there is a relatively wide
range of concentrations at which peroxide will allow the growth and fruiting of mushroom mycelium. The established
mycelium, because of its ability to produce high levels of peroxide-decomposing enzymes, is evidently able to defend itself
against much higher concentrations of peroxide radical than can isolated spores, cells or tiny fragments of multicellular
organisms. So we can add hydrogen peroxide to mushroom cultures, and the mycelium will grow but the small
contaminants will die."
"Growing Mushrooms the Easy Way" by R. Rush Wayne, Ph.D.Hcc