Tea tree oil has same turpintine chemical components
The chemicals in tea tree oil are similar in composition and effect as turpintine, you can buy pharmacutical grade tea tree oil in target pharmacy department for about 5 dollars for a few ounces or buy it at a health food store. I read in many places do not use tea tree oil on cats as they have a sensitivity to it and thier livers have a hard time eliminating the turpintine like chemicals in tea tree oil. Also tea tree is for external use only. Thymol, thyme essential oil also has similar components as turpintine. Listerine has thymol in it as active ingrediant, worms probably don't like any kind of turpin chemical that's why listerine says it kills germs, small organisms.
Tea tree oil is reccomended for external use, it repells and kills bugs, germs and small organisms due to its turpin components. not internally for worms though as MH said, turpintine is a slow poison and I do not know turpins effect on human body or liver. I like the smell of turpin/tea tree oil and thymol as a skin topical, it is antiseptic and is a good external antimicrobal agent or sprinkle it, tea tree oil, around to repell bugs or just use plain listerine as a mouth wash to get some thymol, turpin, effects.
I think wormwood clove GBWH and lots of other foods herbs and spices used in combination over time with clean diet, hygiene and lifestyle changes would work best to kill worms and as anti parasite.