Looks more like citrus leaf skeletonizer; but if a true caterpillar it would have to be the cat of the Swallowtail butterfly; as it is the only butterfly that lays its eggs on citrus. If you google Swallowtail caterpillar you can see the very distinctive coloration and compare with what you have. As for control, physical removal is the simplest method. In Guatemala we have the Swallowtail (Southernmost range); but we also have a couple of species of birds that particularly like them and their caterpillars.

John, these are extremely tiny - not sure if they are swallowtail cats or not. They do hang from threads when knocked off the tree (forgive my ignorance - maybe most caterpillars do this?) The one I killed this morning did the damage to the leaves in the top picture, as they were fine last night.

I found a tiny one on my Eureka after Kelley told me about hers. I wish I had examined it more closely. I vagely remember it having a large head that was differently colored from the body. Bt is organic and can be applied to plants when infested with caterpillars.

Denise, I completely forgot about this - thank you! I just ordered some.