Choose:

File > Export > Desktop Publishing Formats > GEOTIFF/TIFF

Select Idrisi to geoTIFF/Tiff

Also export the palette as we want to keep the colors. Press OK.

Open and register the file with:

File > Open

Select your file and press OK. MapInfo recognizes the coordinates in the Geotif but not the projection, so we have to set it. Change the Category to: Non Earth and Category Members to: Non Earth (meters) (this is the same as a plane projection).