It looks familiar. If it's the weed I am thinking of, it gets tall and big. I don't think it will stand up to regular mowing if it's that one. Might just gradually go away on it's own.
Dave.
Try the Asiatic Dayflower. Pretty common in our parts and should pull out easy.... Asiatic Dayflower (Commelina communis) . My experience is that it inhabits disturbed areas pretty quickly......Gary