When I'm done, I carry the bowl of gritty water outside and use it to water my plants. That way the water does double duty both cleaning the greens and watering the garden.
I should also clarify that usually buy organic greens from the farmers market and don't use any soap when washing them. I just swish them in water to dislodge any dirt (or insect hitchhikers) and let the dirt sink to the bottom of the bowl. I figure the little extra dirt is fine for the garden and probably better overall than letting it go down the drain.
(Image: Emma Christensen)