Fungal infection on cork mount

[JVinOZ]

About a year ago I managed to source pieces of natural cork branches which are ideal for growing many epiphytes which have a tendency to roam.
I have recently noticed a white fungal infection growing on the surface of the sphagnum moss I have used to keep the moisture up to the roots while the plants establish themselves. One other piece of cork has developed a thin purple layer of fungus which is spreading across the surface of the cork.
The fungus does not seem to be inhibiting the root growth of the orchid. It just looks unsightly and with time will assist in the degradation of the mount.
Does anyone know how to get rid of this fungus without having to remove the moss and disturbing the orchid roots?