It's an annual plant, so if you can keep it from going to seed that should eliminate it. As late in the year as it is now, you could mow it and I don't think it could rebound quickly enough to seed.
I did the same thing yesterday. I had lambs quarter to come up thick in one of my plots planted this year. It was close to having viable seed, but I stopped it. I barely clipped the tops of the food plot species and they will rebound quickly, but the lambs quarter was taller and got a good hammering.