Here we have to understand whether information is necessary for the sentence to convey the idea or additional.
Here in option A. located behind the ear is additional information. Thus, it is presented as non essential form separated by comma.
Even without this information we can deliver the intended message. Therefore, presenting this part separated by comma is ok.
Further a habit or the habit is a split. We should use a habit, because we are talking about general habit of smoking not any specific referenced smoking.
C and E can be eliminated.
We can eliminate B and D because located behind the ear is presented as essential information, but in original sentence it is presented as non essential.
In surprising medical news, scientists investigating long-term effects of stroke are reporting that injury to a specific part of the
brain, located behind the ear, can instantly and permanently break a smoking habit.
a. brain, located behind the ear, can instantly and permanently break a smoking habit.
b. brain located behind the ear can instantly and permanently break a smoking habit
c. brain, located behind the ear, can instantly and permanently break the habit of smoking
d. brain located behind the ear, can instantly and permanently break a smoking habit.
e. brain, the one located behind the ear, can instantly and permanently break the habit of smoking