What to do? It's a very small plant that I put out about a week ago. I did a search and didnt find any answers.
Leaf miners are tough to control without extremely heavy doses of specific chemicals to which they have not yet developed resistance or immunity, and I've never had them do enough damage to my plants that I felt the plants' health or productivity was threatened.
Generally, if I do anything at all (and usually I don't), I just pick off and throw the leaves with leaf miner damage into the trash.
I tend to just ignore them. They've never spread widely, they've never harmed anything other than a leaf here or there, and I just leave them for the beneficial insects to take care of.
If you want to read more tips about organic control of leaf miners, see the attached link.
There are very, very, very few insects that I really consider a "threat" in the garden. There are even fewer that I get "wound up" about. How short is the list? In our garden, the only insects that do enough harm that I try to handpick and remove them or otherwise remove them is short and simple: Squash Vine Borers, Squash Bugs, Colorado Potato Beetles, Leaf-Footed Bugs and Stink Bugs. Everything else I just ignore. There always are going to be insects in a garden, and 99% won't do enough damage to be an issue. Almost every insect you see in your garden has some sort of living creature that preys upon it, so if you leave it to Mother Nature, she'll handle it. Of course, this only works if you are not spraying broad-spectrum pesticides (whether chemical or organic in nature) that are killing off your beneficial insects.
Here is a link that might be useful: Organic Control of Leaf Miners