The angle at which light is reflected off from the table lamp towards mirror B is at an angle which will not allow the image of the lamp to reach the observer (eye). As the law of reflection states that angle of incidence from the normal line is equal to to the angle of reflection from the normal line.
You might be right. Although some light can be seen, one cannot be certain it comes from the table lamp. You might be seeing the light reflection but not the lamp itself. Cat would be a fool proof answer.