What you are experiencing isn't normal. All my lenses fit on the D800 and other Nikon bodies) with no play although there is some very slight rotational "give". I'd have this checked out by the Nikon service center.
BTW, the TC-17E is an excellent product. On the 300mm F/2.8 I cannot see any photographically significant compromise to image quality - like getting a top 500mm lens for a few hundred bucks.