Moss/Fungus/Something on my soil

The 3 flats of Vinca are growing very strong. But I'm a bit concerned on the continued proliferation of this white mossy/fungus on the top of the soil. Can you identify and give a good way to treat? I was thinking of removing the top layer of soil with my fingers or spoon and then drenching the soil with a 1 tbsp 3% Hydrogen peroxide to 1 quart water combo. But maybe that is too mild of a solution. I've been bottom watering the seedlings with this combination of h202 + water since they were seeds, removing them from the water when the top of the soil started to become moist. I don't know if drenching it with this combo from the top instead of bottom watering might make the difference?

Had to show how beautiful the 2 flats are and why resolving this issue is important to me :). I'm not sure if left untreated if the moss can eventually kill the vinca? The vinca will be in the ground in about 3 weeks, at which point I assume the moss will die off.

I stir the surface with a toothpick and spray with HP/water 1:10 and it gets rid of it. Hope this helps.

dahlianut,
Do you use the standard 3% bottle of HP or a stronger version?

I would just use straight up 3%, no dilution.

And there's no concern with that high of HP to damaging the plants either by their roots sucking it up or the spray getting on some of their leaves or stem?

You can use HP instead of water it just adds extra oxygen.

I use the standard 3% solution lancestorm