Believe it or not, not every parent is looking for a grammar school place. There are a number of schools which use use selective tests to allocate a minority of their places, as well as the Harris Academies which allocate their spaces in bands according to their NVR test. If you like Greenshaw school, and live outside the usual catchment then entry via the selective test can be a useful way of getting a place.
The trust running Greenshaw also runs Edenham in Croydon which also has the selective entry scheme.
Parents who are applying to numerous schools without them fully might be in for a surprise though. I don't think that there is a South London equivalent of DAO for example.
Please, someone come along with data to scotch this idea completely, but if Greenshaw is anything like the partially-selective school five miles away from us, just over the border into the next LA, most of those taking the 'selective' route are pupils from catchments in our LA who wouldn't get in on distance. They are not necessarily even any more academically able than all of what is left of the catchment population after some have been 'creamed off' by our grammar schools, they just did well enough to beat enough of the competition off to get one of the up to 15% selective places. And that school does do their admissions according to their admission criteria, cutting the intake off at PAN, rather than endlessly stretching it like DAO if there happen to be too many applicants in a higher but less 'desired' category.