Homeowner Representative: Statistics show that burglars often target houses that appear unoccupied. Therefore, when home

Premise: Statistics show that burglars often target houses that appear unoccupied.
Conclusion: we recommend that they leave lights on, to give the impression that the house is occupied, when homeowners are away
Counter-Argument: The same lights continuously on all night long with no change give a potential burglar a clear signal that the house is unoccupied.

Here it can be clearly seen that the 'counter argument' is attacking directly the conclusion of Homeowner Representative.
Let's jump to options now:

A) calling into question an unstated assumption
Calling into question? Yes. for sure, it is questioning the reliability of the conclusion.
An unstated assumption? wait a minute! it is attacking directly the conclusion and not the unstated assumption. Infact, we don't need to focus on assumption here anyway. Hence, A out.

B) pointing out an undesired effect of a recommendation
Yes. looks perfect. even though the Housemaker representative tries resolving the issue by giving a recommendation but the Crime expert actually showed the negative effect of that recommendation.
Looks great. Let's keep it for now.

C) presenting new evidence that calls the conclusion into question
It actually call the conclusion into question. which makes this option an ideal next preferred option. but look closely - New Evidence. what new evidence. There no new evidence stated in the second para. What the crime expert stated was not a new evidence but fact, which was ignored earlier.
For that reason C out.

D) explaining that a reputed effect is actually a cause
Reputed effect is a cause? umm. okay. it is stating that the outcome of keeping lights on, becomes the cause that the thief will get attracted more. Makes sense. Okay, Let's hold on to D for now.

E) demonstrating that the conclusion is true, but not for the reasons cited
It is actual a counter argument attacking the conclusion so in short it is saying that the conclusion is not true. E out.

Lets compare B and D now.
B) pointing out an undesired effect of a recommendation
D) explaining that a reputed effect is actually a cause

These 2 option are actually very close with a very subtle difference (IMO)

So what D actually means is If the lights are on the whole night will attract more burglar to come and steal. which indirectly means that even if someone is at home and the light are ON for whole night (for any reason), the burglars will come to steal things. or to make it more simple what it says is:
if the lights are ON, burglars will come.

But the actual case is - if the lights are on and there is no movement then the thieves come. Only keeping the lights on will not invite the Burglars, but a combination of Lights On and No movement/No change will.
Hence, for that reason, B over D.

very close option.