Peat mold is a non-harmful type of fungal growth that forms in decaying organic material, like peat. Therefore it won’t grow onto your living plants - it will stay in the growing media.
SIGNS YOUR PLANT HAS PEAT MOLD
White mold may develop on the surface of the pot
Alternatively, you may see powdery yellow-orange growth on the peat surface
You might notice an odor surrounding the pot

WHAT TO DO NOW
Even if Peat Mold isn’t harmful to your houseplants, it can be unsightly, so you may still wish to try and remove the mold.
Note that typically available fungicides do not tend to be effective against this type of mold.
To get rid of it you can try this:
Remove the visible fungus on the top soil
Water from beneath for a while
Make sure that the soil dries up between waterings (within your plant's accepted range)
When it's time to repot - change ALL soil and clean out the pot thoroughly . Mold residues may be present in the soil even if they’re not visible, so by cleaning out all the old soil, you’re reducing the chance of the fungus coming back. The gentlest way of removing all the soil from a plant is by rinsing the roots in water.
Mold develops where conditions are humid and moist, so you can work to establish slightly drier conditions for your plant to prevent re-growth of the mold. Reduce the amount of water you give to your plant, or reduce the frequency of waterings for a while (although make sure that your plant is still getting enough water), and increase the air flow around your plant. This will help prevent the mold from establishing itself into a layer on the surface, as this could potentially interfere with the soil’s drainage/ability to take up water.
QUESTIONS
HOW CAN I PREVENT THIS FROM HAPPENING AGAIN? As molds develop in damp conditions, try to make sure you’re not overwatering your plant. If the plant type allows it, then you can try letting the soil dry out between waterings (check in the plant’s Info tab to see if this is okay for each particular plant).
HOW CAN I MAKE THE SOIL ODOR GO AWAY? If your soil has an odor, exposing it to better airflow and allowing it to dry out will help it to go away faster. Once the soil has dried out, the odor should be more or less gone, or at least much less strong.