I was having this same issue for a new customer discount code and them stacking on top of a sale I was having with the prices discounted (strike through price). I figured out an easy way so i don't constantly have to edit the eligible collection for the new customer discount.
I added an eligible collection for the discount code. On the collection for the discount CONDITION TYPE--> COMPARE AT PRICE --> IS EMPTY
This will make any marked down products ineligible for the discount code.
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