I had this same problem and its because the background of the texture map is white. There are several ways to handle this. In 3ds max, go into the material editor for the object, there is a color selector to the right of the map file name. Change it to black. An alternate that may work that I haven't tried, assuming you're importing an obj file, in the import window, under materials is a button that says "force black ambient" I think that does the same. Worst case scenario you can photoshop the map file and fill the background with a color similar to your object.. I think
Hope this helps