Answer
Does turning off location services remove GPS from photos I already took?
No. It only changes what happens to future photos. Coordinates were written into each existing file at the moment it was taken, and they are still there.
Updated
Location services control whether the camera app asks for a fix when you press the shutter. Turning the setting off stops that request. It does not reach back into files that were written while it was on — those coordinates are bytes inside each photo, and changing a system preference does not rewrite them.
This catches people out at exactly the wrong moment, because the realisation usually arrives when someone is about to share an old photo. The setting gets switched off, and the file being shared is one of the thousands taken before that.
Your existing library needs handling as a library. Photos taken across years, on holiday, at home, at work, each carrying a fix from wherever you were standing. The pattern across the whole set says considerably more than any single file does — a home address is simply the place that appears most often, late at night.
For a backlog, the bulk remover takes hundreds of files at once and returns them as a single ZIP, without any of them leaving your device. If you would rather keep the camera settings and exposure data and lose only the coordinates, the GPS remover does exactly that.
It is also worth checking what the setting actually did. Some devices offer per-app location permissions that are easy to leave enabled for the camera while believing they are off globally — open a recent photo in the viewer and see whether coordinates are still being written.
More on this: GPS location remover.
Terms used here: EXIF.