Cleome belongs to the Brassica family, so you probably have Cabbage Moth (Mamestra brassicae) caterpillers munching on them.

Sharon

It also could be the (Pieris rapae) Cabbage White Butterfly too. They love to munch on brassicas as well.

Here is a link that might be useful: Pieris rapae

Don't worry about a name....take a hose and wash them off....then spray with insecticidal soap.
Linda C

Don't worry about a name
My goodness, not an intelligent advice to give...it's always good to know what kind of insect your dealing with before using any kind of pesticide/ insecticide!

Sharon

Ahhhh. moths. ARGH. Okay- I'll hose them down. I've been picking them off one by one, but they are really hard to see. I put some slug bait out, but will that help if it is caterpillars?

Not to be nitpicky, but Cleome doesn't belong in the Brassicaceae family, but the closely related Capperidaceae. ;-) Many of the same pests will visit both families, as they share some chemical compounds.

Another possiblity would be sawfly larvae, which look very much like caterpillers. Either way, insecticidal soap would be what I would use to spray your plants. Make sure that the product actually gets on the pests, or it will be a waste of your effort. Insecticidal soaps, once dry, do nothing.

Slug bait will have no effect on caterpillars. I hope, at least, that you put out the environmentally non toxic baits that are readily available.

Cabbage white butterflies are lovely, but I don't blame you for not wishing to see your Cleome ruined.

Rhizo.....Cleome is a genus traditionally included in the family Capparaceae. Some recent classifications (e.g. the APG II system) have included the Capparaceae within Brassicaceae, while others classifications have transferred Cleome (along with other related genera) to its own family Cleomaceae, separate from both Capparaceae and Brassicaceae. ;-)

Yes, I absolutely put the environmentally friendly one down. I got it at Gardener's Supply. Well, maybe I should just leave them! They are welcome to some, but they are really eating them all up. I don't know if the plants can rebound or not