Hi Terrie,
does not sound good for the Luna Moth caterpillar..Even picking off the eggs does not mean it will be ok.. :( A lot of times the eggs are also inside the caterpillar and the caterpillar will die when the flies, etc hatch.. :(
It is worth a try to see what happens, Best of Luck..
I found this article online, but I disagree about how good those Flies are,I myself rather have tons of caterpillars..
Greetings
Suanne(SUE)
Are you sure it is a Luna caterpillar?? Not a Tomato-Hornworm??

Here is a link that might be useful: eggs on caterpillars

Thanks, Sue! That pic looks exactly like what we have! I thought it was a luna moth (i.e. giant green caterpillar = luna moth), never having seen this tomato bug before, but now I'm not sure. It probably is the Tomato Hornworm. I still feel bad for him though...

Those are not eggs, but 'cocoons'. Some time ago, the caterpillar was parasitized by a tiny female Braconid wasp. She deposited eggs under the skin of the caterpillar, which hatched into minute (as you can imagine) larvae. These wasp larvae feed on the caterpillar from the inside and when they are ready to pupate (turn from larvae to adult Braconid), they create those little white cocoons on the outside of the caterpillar.

Only the Braconid wasp makes those types of cocoons, though there are certainly other parasites of caterpillars out there.

You can tell if your caterpillar is a hornworm or not by the little horn on it's back end. If it's a red horn, it is a Tobacco Hornworm, the most commonly seen. If black in color, it's a Tomato Hornworm.

The caterpillar of the beautiful Luna moth is big and green but has no 'horn'.

Most people are very happy to find a parasitized hornworm on their tomatoes.

Thanks RHIZO
for correcting me, of course they are cocoons, not eggs..I found another webpage which explains the entire lifecycle..
Greetings
Susanne(SUE)

Here is a link that might be useful: Lifecycle