Native or otherwise, they make quite a mess. I have cut them back and will now mow the shoreline, and and keep cutting them as close to the bottom for the ones in the water. This is supposed to drown them. I may end up using the glove of death if they keep popping up on land. The areas in the water where they were are like booby traps with their sharp stalks sticking up. You need stout footwear just to wade into these areas, and the roots are impossible to remove without a backhoe or some such equipment.