"Leaf miners" is the correct answer, but that really describes several different insects that have the same feeding behavior, some are not at all related insects! For example, certain moths and sawflies.
You can try the neem / soap.
Also effective are Spinosad and Bacillus thuringiensis (biologicals, based on bacteria, safe to humans) though the miners have to ingest these at the right time to be most effective.
As an added step, if just a few leaves are affected, remove and destroy the leaf.