If you think that is the correct ID, then, yes - destruction of the plant is probably what you need to do or regret it later if you don't. I take chances with things I find growing naturally and so far those I've deliberately tried haven't tried to take over the world. There is one I accidentally relocated when getting some sand that I've never been able to remove and another that moved in on some San Augustine plugs that is permanent, I guess. Sort of like the Bermuda grass which is ubiquitous. Sometimes something looks good, but is just way too much trouble to keep out of areas where it's not welcome.