No need to replace it. You have an overgrowth of fungus, but it will balance out. Fungus breaks down woody organic material, so if the compost wasn't completely broken down and had lots of wood it will grow fungus but not forever. Tilling it can help because fungus grows better when left undisturbed. It will balance out eventually whether you stir it up or not, but it happens faster if you do.

The white stuff is just the underground part of the fungus.

It's not going to hurt anything.

Thanks for the replies...now if that cooler weather can be as helpful....