Answer: Termites are interested in the cellulose fibers inside the vegetable stems, not the living tissues. The problem with your situation is that you will not find a product, organic or otherwise, labeled for use in vegetables to control termites! The label is the final authority so we can't recommend even an organic product for termite control in veggies. Applications of organic insecticides to control other pests on your veggies will likely have a detrimental effect on the termites.
I have had termites in my okra and some other plant stems but have never considered them to be causing serious damage to plant health. I would suggest you keep the garden clean of woody debris and turn the soil periodically to make for a less hospitable homesite for the termites. Good luck with your garden.
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