For my part you are welcome, mpc.
Presuming dots and factor shape as closed paths with the same fill colour and no stroke (if the factor shape has another fill colour, you will need to reset the dot fill colour, and if the factor shape has a stroke instead of a fill, you will need to change the dots from that stroke to the original fill), you may get most of the unwanted dots deleted easily if you:
1) Select the factor shape path and Object>Path>Offset Path, using an offset that makes the outer path fully enclose all dots that are partly inside the factor shape;
2) Lock the factor shape and bring the new offset path to the front (Ctrl/Cmd+X+F);
3) Select everything and Pathfinder>Minus Front, this should turn the offset path and all the dots (partially) within it into a Compound Path, with all the outlying dots deleted;
4) Object>Compound>Release, Ungroup, and delete the offset path (with its funny shape);
5) Delete the remaining unwanted dots individually for best fit as described;
6) Unlock and Hide or delete the factor shape.