The previous owner left a few prolific varieties. Star of Bethlehem I know from past experience is just about impossible to get rid of. Planting it, and cleome, were two big mistakes I made.
Cleome, or “Spider Flower,” is well thought-of by many, but I found it to be a nuisance after a couple of years. The flowers (to me, at least) had a skunky aroma. And they self-seeded like mad.
Star of Bethlehem is beautiful and invasive. In the early to mid Spring it covers its area in a brilliant white display of anemone-like flowers. And then it’s off to the races. It spreads underground by means of pellet-sized bulbs. I could dig up a trowelful of soil any time of year and pull out a hundred of them. I’m not sure they ever really went away, I haven’t been by that house yet this year.