You will likely have to resort to using a systemic herbicide to kill the Houttuynia (Fish Mint, Chameleon Plant) roots. Even though it can work well, repeat treatments will likely be necessary for established patches of this aggressive weed. Follow all label directions for the most low-risk, effective application of the chemical chosen.

Some products may allow for (or even encourage) the addition of a surfactant upon mixing a solution for application. Surfactants, also called spreader-stickers or adjuvants, are additives that help a herbicide adhere to the leaves (in this case) or work more effectively. These products are sold alongside pesticides in garden centers since the two are often combined for certain uses, though not every product benefits from their use, so always verify this with the label usage details.

Early autumn may be the most efficient time of year to attempt herbicide treatments, since the plant's deciduous leaves will be transporting more carbohydrates in the sap down into the roots for winter storage, and the absorbed chemical will then be able to "hitch a ride" more easily into the root system to cause dieback. Be aware that plants successfully treated (any time of year) might not show obvious signs of dieback for days or even a week or more after application, but it doesn't mean the application isn't working.

If you wish to avoid herbicides, your only recourse will be to physically remove what you can by digging-out roots and to constantly keep trimmed-down all above-ground growth so the plant cannot photosynthesize. Every time it can regrow for a while the plant is recharging the root “batteries,” so to speak, for continued regrowth. That battery is depleted a bit every time the plant is forced to replace foliage, so if you can keep "discharging" that battery by making it keep regrowing without being able to photosynthesize, eventually it will starve and stop returning. This method might take years to achieve full eradication for well-established weeds, and will only work well if you have full access to the continuous patch. (For example, if part of the plant's spread continues into a neighbor's yard that isn't able to be controlled because you can't access it or they aren't willing to help combat it, that foliage could still fuel regrowth back onto your side unless you install some sort of barrier along the property line.)

Denying the foliage light instead by smothering the patch with a light-blocking tarp probably won't work as well in this case as it might for other weeds because this species could just keep creeping outside of the covered area to resume growing. Plus, any desirable plants growing among its leaves would be killed as well by the tarp. (Granted, desirable plants would also be damaged or killed by herbicide if directly exposed.)

Miri

You're welcome.