Rubbing the seeds was the right move... in fact, you may want to rub or agitate them even more. You want to break off as many of the tiny stems as possible. Ideally you would need two strainers. The first one would have holes just large enough for the seeds to pass through, to sort out larger debris. Then shake or stir the seeds in a strainer with holes just smaller than the seeds, to remove the stems. This might take awhile, since the long stems need to pass through standing up. Doing this over a mixing bowl will help to track your progress... and missing a few is no big deal.

Alternatively, you could try to winnow the seeds outside, in a light breeze (a strong breeze will blow the seeds as well). Not as easy or effective as straining, and you would probably lose a little seed; but better for cleaning large quantities.

Personally, I prefer using strainers.