I've seen this problem numerous time and everything that people have done has not removed them.

This is not an easy task, the little disk that attaches to the surface are very hard to totally remove, I have seen somewhere that soaking them with cooking oil "using a paint brush or other means" letting it soak in a few minutes, and using a stiff scrub brush would facilitate the task.

The best thing I have found worked for me is the following:
Soak the siding with water, scrub with Bull steel wool, or SOS pads, it will remove the remenence. It will leave white dots, however we plan on painting over the siding and renewing the colour anyways.
This is the best thing I have found to work. I tried ZEP house cleaner, a pressure washer, soaking it in 1 part bleach, 2 parts water, sanding it with an electric sander, or by hand, nothing!
Try the steel wool, or SOS pads.