I'm pretty sure that's a leaf sucking critter that's doing the damage. It's hard to tell from the photo, do the little black dots rub off, if they do, is what rubs off juicy or dry?
Aphids and spider mites sometimes infest oregano plants. You can control mild infestations with a strong spray of water from a hose every other day until the insects are gone. Once knocked off the plant, these insects are unable to return. For stubborn infestations, use insecticidal soap or neem oil spray.