Squish 'em! And/or give 'em a good dose of garlic spray. Put plenty of chillies in.

GARLIC SPRAY:
Soak 1/2 cup crushed garlic cloves in 1/2 cup vegetable oil for one week. Add a little liquid soap and dilute the mixture - 1 part mixture to 10 parts water. Garlic spay will kill and repel aphids, woolly aphids, bean fly, stink bugs, crickets, grasshoppers, red spider mite, sawfly larvae, scale, snails, slugs, thrips and caterpillars, mosquitoes and ticks, the adult moths of leaf-miners and mealy bugs. It is an effective fungicide when used 3-4 times a week against potato blight and damping off.
OR
Crush 100g garlic, 2 chillies and 2 onions and cover with water for 24 hours. Strain and add enough water to make up 2 litres.

Will these sprays affect the taste of the mint and basil?

Your caterpillars looks to be one of the inchworms...found on many different kinds of plants. You ought to be able to spray them off with plain water from the hose. You could also use insecticidal soap. I suggest that you purchase the commercial product, so that you can take advantage of actual directions and dilution rates.

There are additives in most dish detergents that can harm plant tissues, another reason to avoid their use on our plants. The commercial insecticidal soaps are true soaps, not detergents.