Bugs will make a meal out of pepper leaves just like other bugs will go after the peppers themselves. Healthy leaves are important to the overall health of the plant. Most of the insects will not do severe damage, but a heavy infestation all eating at the same time, no matter what insect it is, is something you want to avoid.
Several bugs will make a meal out of the pepper plant leaves. Cutworms will go after the leaves when the plant is still a seedling and can do the most damage. Armyworms, fruitworms, flea beetles, hornworms and whiteflies also think of pepper plant leaves as a meal.
Keep the area around the garden free from low lying brush that insects could winter over in. Look for varieties that are resistant to insects and diseases. Plant the seedlings in a raised bed after the soil temperature is 55 degrees Fahrenheit.
Hornworms are large and can be picked off by hand. For the other bugs, spray the leaves with soapy water. A heavy infestation will require the use of pesticides. Check with your local cooperative extension or county agent about what is legal in your area.