I purchased a Peace Lily, but I didn't have a chance to repot it yet. However at the beginning of the week I saw some gray fuzz and and also mites and sprayed it with Bayer Insect Disease and Mite Control. It helped for a day or so but I saw the same gray fuzz yesterday.
Should I repot the plant and treat or should I return it to the store where I bought it?
@JM Sorry was an error click
That is mold. It digests the damp organic matter in the potting soil, not the plant. While it won't harm the plant, it is often a sing of constant damp, which isn't healthy. In addition to your fungicide application, allow a layer of potting mix (about 1/2" deep) to dry out between every watering. When you water, water very thoroughly. And while your control product covers most fungus, it won't be as potent as a specialized complex fungicide.
Your peace lily likes high humidity, but this also encourages mold, so help prevent it by keeping it in an open area, preferably with some light air circulation going on.
Also, about repotting, make sure your plant actually needs it first. You can damage a plant by moving it into too large a pot before it is ready. Don't return the plant. The mold is not their fault, and is fairly easy to take care of.
If the Bayer doesn't work completely, you might consider mixing a few tablespoons of neem, canola or soybean (vegetable oil) with water in a spray bottle (shake it up every few to several sprays) and occasionally spray the soil surface every week or two, perhaps, for a while. Spraying the plant with the same (especially the undersides of the leaves and new growth) should help against mites, too. It may outright kill the mites, but whatever the case, it should make the leaves too sticky for the mites to move much (kind of like a sticky fly strip).
You might also consider giving the soil more light (especially sunlight), but bright light, whatever the case. This should help to reduce mold and fungus generally. If it's warm enough to take the plant outside in the day, you can try that. Just make sure it's not too harsh an environment for your plant and that new pests aren't about to infest your plant.
Air circulation should help. Soil drainage should help.
New soil could eliminate the fungus problem (not the mites), if it's the right kind, and if your environment isn't spreading mold to your soil, but as J. Musser said, it may or may not shock or kill your plant.
