A TIFF image created with GRIDIMAGE or CONVERTIMAGE appears offset half a pixel width down and to the right when displayed in ArcMap.
GRIDIMAGE and CONVERTIMAGE create GeoTIFF images that don't include raster space information in the image tags.
When an image world file is present, Workstation ArcInfo reads the world file instead of the GeoTIFF tags. The world file default raster space, PixelIsPoint, indicates that the image coordinates are referenced from the center of the upper left pixel.
ArcMap reads the GeoTIFF tags instead of the world file and defaults to the PixelIsArea raster space. This references the image from the upper left corner of the upper left pixel. The difference in the default raster space accounts for the half pixel offset.