It was not explicitly set out but given in the Wikipedia article linked; the reason D gets no detections when the bomb is dud, (same as if not there/ no obstruction ) is destructive interference.
Proposed explanation: When a live bomb is obstructing the path, the sub photon member is halted so can not participate in destructive interference.
Same applies for this apparatus without a bomb but a mirror placed before the top mirror, deflecting the beam to a third detector. This also allows D detections. However rather than it being a non local effect on a beam that has not encountered the inserted mirror, it is due to deflection of the sub photon members to the third detector. So, being unable to destructively interfere.