If there is a missing tile, it will not automatically be removed from the footprint. In other words there will not be a hole in the footprint polygon where the tile is missing. It is assumed that all the tiles are present. When viewing the image service the missing area will be represented by the background color defined in the image service definition properties. You can manually edit the footprint using the editing tools in ArcMap, to clip out the missing tile area within the footprint polygon. Be sure to recalculate the boundary after altering the footprint.