Answer: The growth is a symptom of excess humidity. You'd be wise to remove the covers and leave them off. Sometimes plastic covers are used to increase humidity and keep them from drying out, but they should be removed once your plants have sprouted. Once you've lowered the humidity the mold might die on its own, but you can remove it carefully with a stick without harming the seedlings. It's also a good idea to use a seed-starting soil (Pro-Mix or the like) rather than potting soil, which is heavy and often gets too wet, actually causing seeds to rot. I know from experience that pepper seedlings prefer good drainage, and may show much growth in heavy, wet soil, even with a heat mat. Also, excess moisture often invites damping off disease, which causes seedings to keel over as if they'd been felled by a logger. Hope your peppers do fine!
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