Without looking at this plant with a hand-lens it’s impossible to be sure, but this type of mottled leaves is typical of the damage done by either a sucking insect or spider mites. The reason that leaves end up stippled and pale with such infestations is that the insect or mite pierce the leaf again and again as they feed, and this kills the cells in the leaf. Initially the leaves just look stippled, but over time the entire leaf can die.
Leaf hoppers, lacewings and whitefly are three insects that suck plant juices and cause similar damage. If you look closely, or with a hand-lens, and see webs it’s likely that spider mites are the cause.
Since most people want to eat their herbs you of course don’t want to use systemic or other chemical insecticides. Also, mites aren’t killed by some insecticides. You could use one of the insecticide/miticides made from neem or cinnamon however. Another good practice in such situations is to spray the plant with a hard stream of water once a week.
How can we thus control or get rid of the pests on an already infected plant.