Pick caterpillars off and dispose of in a manner you can live with. Also, Bacillus thuringiensis is a biological control agent, and there are insecticides. Holly leafminers are midges in disguise. Female midges make wee slits in lower leaf surfaces and lay eggs in spring. Larvae hatch and feed inside of leaves, and you see the marks made by their winding tunnels.
Adults eat leaves, leaving small dimple-type scars.
Pick and destroy affected leaves. Eastern tent caterpillar shows itself with large blobs of web in trees in early spring, the result of last year's eggs. If you're looking at the web when eggs hatch, you'll see a gazillion caterpillars squirming inside and moving out and along tree branches. They munch new leaves and grow to 1-2 inches in about six weeks and go off to spin white cocoons. Reddish-brown moths are the adult form.