Once it has plenty of new leaves, you can cut a few old ones off. That will be strictly a cosmetic operation and will not affect the growth of peppers one way or the other. On the other hand, if you cut the leaves off too soon, before it has enough others, it will slow down the growth of the plants. The leaves are how the plant collects energy from sunshine to fuel its growth and other processes. The old leaves, though spotted, still have plenty of good green areas left to do the work.
What you said confirms my suggestion. It was indoors at Sam's so not used to full bright sunshine. The new leaves that emerge are adapted to full sun. To avoid this problem in the future, just let your new plants adapt to full sun a bit gradually, just a few hours and first and then increasing.