Not eggs, caterpillar poop from eating and eating and eating your plants.

FataMorgana

are they bad caterpillars? or are they going to turn into butterflies??

So caterpillars that eventually turn into butterfies are GOOD? I am so mystified by that philosophy....not that I disagree entirely.

Some of the most beautiful insects in the world are moths, by the way, not butterflies. And not all butterflies are pretty. Most of the adults act as accidental pollinators, visiting an assortment of flowers day (butterflies) and night (moths) .

The larvae (caterpillars) of both categories have one job and they all work very hard at it....they EAT! If the caterpillar of the most splendid butterfly on the planet was devouring my one and only veggie plant, I'd have to turn him into bird food. :-) I remove caterpillars from my food plants but do nothing to control them elsewhere. As a matter of fact, I grow seedling citrus expressly for the Giant Swallowtail. Boy, do they ever look awful by the time the caterpillars get done with them!

Your little cat is an ordinary cabbage looper, fairly common on basil. It turns into an ordinary little moth. It's up to you about where to draw the line on caterpillar tolerance. Personally....I'm fond of my basil.

I had a bad problem with loopers a couple seasons ago. They almost skeletonized two of my toms that were next to the building. Where there's one, there's usually many more. They're hard to spot because of their color, blending in with the leaves they're devouring. I sprayed with Bt and stopped the carnage, but you could also just keep picking and relocating them if you don't want to spray or dust.
Right now I'm trying to save some dwarf sunflowers from climbing cutworms. I had to go out at night to find what was munching them and found some on the sunflowers, marigolds, petunias and catnip. They got tossed into the parking lot for the toads and the next day I pulled out the Bt to(hopefully)take care of the rest. These plant are near the front door and I think that the more I have the light on in the evening(the parking lot lights are not working) the more moths come around laying eggs and the toads can't get them all. I could be wrong, but that's just my guess.

Ghoghunter....I did not say it was the caterpillar of a Cabbage White butterfly....but that of a Cabbage Looper, which will turn into plain little moth. The former critter largely feeds on members of the Brassica family, but the looper is very much an equal opportunity caterpillar!