Need to identify this apparent ground cover plant that dies off in the winter and returns in the spring. Also wish to know how to contain or eliminate it. Attached pictures show it growing inside Heather (and blooming), but it also overruns just about everything in its path including the lawn, and has a strong fragrance.
Your mystery plant is chameleon plant (Houttuynia cordata), an aggressive groundcover which, as you’ve discovered, can take over garden space unless contained on all sides by an expanse of concrete. It’s a perennial that dies to the ground for the winter and, then, regrows in spring.
You can get rid of it by digging out its vigorous root system, perhaps combining that with herbicide applications. Whatever your choice, you will need to be persistent for several years because any small piece of root that you miss will grow another day. Promptly remove any regrowth, either by digging or spraying.
The herbicide (weed killer) glyphosate, the active ingredient in Roundup and other readily available products, will work but will also kill all other nearby plants which it contacts. For example, if you spray the chameleon plant which is in the lawn, the herbicide will also kill the surrounding grass. (August would be a good time to use glyphosate.)