Looks like spider mite damage. There is no need to destroy your plants. You can cut them back if you don't like the appearance. Google prevention/treatment. They are still perfectly safe to eat if you wash them.

I'm a bit late for this discussion. But I think the problem was water stress. They ran short for a brief time.

Mite damage would be fine stippling, not patchy as shown.

And if it was mites, you should have been able to see them on the backs of the leaves.

OK maybe not spider mites but I still think it is a pest rather than a cultural issue. What about leaf hopper?

Here is a link that might be useful: Leaf hopper on Oregano.

Leafhopper damage is stippling.

The damage in your image appears as if the affected areas are sunken. If so, *not* leafhoppers.

It's hard to see but I didn't notice any sunken areas, just discoloured speckles. Maybe we can ask for a closer view?