"Chufa" is also called "yellow nutsedge". Its latin name is Cyperus esculentus. The "extremely invasive" species is purple nutsedge (Cyperus rotundus).
Both are actually very much hated by the agricultural and golf industry. However, very few people seem to realize that yellow nutsedge is actually native to North America. In fact, it's quite likely purple nutsedge is as well. It's hard to tell with purple nutsedge because both have extremely wide distributions (we know yellow nutsedge is native for sure, just not the cultivar you're probably growing for food).
It's one of those crappy cases where a native species legally classified as an invasive because it suits the interests of the agricultural industry.
