This appears to be stippling damage, which is caused by insects that feed on plant sap or juices. Thrips cause stippling, as do leafhoppers and some stink bugs. Either could be present on the thyme, though thrips are more likely because they're a more common and universal plant pest that are harder to see. Plus, they tend to leave tiny dots of black residue on the leaves where leafhoppers would not, which we think we see in the photos.

If you roughly brush against the plant stems you might cause any leafhoppers present to jump or fly off, which would help you determine which insect is present. Thrips can jump or fly as well, but are so much smaller that they're hard to see this way. Instead, if you sharply tap thyme stems over a white piece of paper, you may dislodge thrips onto the sheet that will be easier to see as they walk around. They would be pale yellow or black and shaped like a grain of rice, but only a couple of millimeters long.

Thrips are hunted by several small predatory insects, but if they're causing too much damage, they can be suppressed with applications of horticultural oil or insecticidal soap. Follow label directions to not only make sure the product is safe for use on edible plants, but that you apply it at the right time and in the right way. For instance, spraying while temperatures are above 85 degrees may cause leaf damage, and all plant surfaces need to be thoroughly coated in order for a treatment to be effective. In either case, several treatments will likely be needed.

Leaves do not heal from damage, so you may not see obvious improvement right away even if the sprays are working. New growth should remain unscathed, though, if the insects have been suppressed. The injured leaves should be safe to eat if rinsed normally. (Pay attention to any label details about pre-harvest interval, which tells you how long you must wait between the latest treatment and harvesting. It could be zero days, but sometimes it's one or more days.)

If you prefer a chemical-free solution, trim back the damaged growth and the plant should recover well if its roots are otherwise healthy. Thyme thrives will full sun and good drainage, so that should help it rebound well. You can try trapping some thrips on sticky cards, though it's more of a monitoring tool to detect outbreaks than a way to eliminate a population. Garden centers usually stock these, which are simply an index card-sized card covered in adhesive on both sides, which is either held up on a stake in the plant pot or hung on a hook above the plant. Most sticky cards are bright yellow because several pest insects are drawn to that bright color, but there is a blue version specifically for thrips, which for some reason is a color they are more attracted to.

Since you mentioned this is a fairly new plant, the pests causing the damage may have been more prevalent at the nursery than they will be at home, which means they may decline on their own over time. This is partly because herbs are often stocked in a greenhouse, and the warmer temperatures greenhouses experience can unintentionally support pest insect population booms before their predators can catch up. Growers tend not to preventatively spray herbs for sale since they know most customers intend to cook with them.

Miri