Short term, handpick as many as you can and squish them. I cannot say for sure if this is a true caterpillar (others here may be able to visually identify it) but I'd say it's very likely. For caterpillars, spraying or dusting with BT (Bacillus thuringiensis) is the real way to go. It is effective on many species of caterpillars, not just tomato hornworm. Most garden centers have this product. BT is just a bacteria that is harmless to humans, pets, etc -- but not so harmless to caterpillars :) It's good to have some on hand in case of hornworm, which can strip a whole plant very, very quickly.

Yep. Caterpillar.

Beyond the above suggestion to squish them, you can flick them into soapy water.

And when it comes to Bt, it must be applied before caterpillars are half-grown. If applied later than that, the cats can continue their development into adults.

And the cat in your photo is too old.