These white striations are actually stress marks or "corking." Their appearance usually indicates that the pepper is ripe and ready to pick! They aren't harmful in any way and don't affect the flavor of the pepper, though some people argue that corking indicates a hotter pepper.
Now that we know what this is, we've also noticed these marks on some of the peppers (both sweet and hot varieties) that we've picked up at the farmer's market. Good to know that even the professionals get corking on their peppers!
(Image: Emma Christensen for the Kitchn)