Grips are a wonderful tool to modify objects with and the most common way to use them is to stretch a selected grip to a new position.  When you select a grip and make it hot, you are actually selecting the grip as the base point for your edit.  This pre-selected base point is fine for most edits, but occasionally you need to use another point for the base point of the stretch or other grip edit commands.  After selecting a grip, look at the command line and you will find your answer.  The first option is Base point!  Enter B to enact the option and select your base point away from the grip.  You can also right-click and select base point from the drop popup menu.