I have a solution that i have been using in AutoCAD MAP 2013. i am not sure what you are using.
For AutoCAD MAP 2013, once you "connect" the tiff file you might be observing the black background surrounding your image. In order to get rid of it open display manager and right click the respective tiff file connection and select "Edit Style". A new dialogue window will pop up. Here you will notice a "transparent" button. Select it. In the new window select " Select <". Now select the back boundary which you want to remove.. Hit "OK". Now select apply in the "Edit Style" window dialogue. MAP will automatically remove the background for you.
Do share if it worked for you