Garden Pests and Diseases: webby caterpillars on my baptisia, 1 by floating_stump

floating_stump wrote:
I discovered these worms all over my false indigo yesterday. They're yellowish green, with black and white spots. They make webs, but not particularly dense ones, like tent caterpillars. Most of the ones I saw were one to two inches long. I snipped all the ones I could find with my scissors (I was cutting out the dead/eaten branches anyway) but I knew I had missed many. Tonight, I found many more, plus several swarms of tiny ones.

What are they, and more importantly, what do I do about them? I could probably cut the affected branches out, put them in something and then burn them, but I doubt I'd get them all, since some of them could fall off and escape.