This is a strengthen question and, more specifically, the stem asks us to strengthen the conclusion. This is important because this may not require us to analyze the reasoning per se but rather just evaluate how an answer choice can strengthen the main point. Either way, this stimulus does present an actual argument and deconstructing it is good practice nonetheless.
It is difficult for physicians to judge exactly how thorough they should be
→
It is generally unwise for patients to have medical checkups when they do not feel ill
The bolded is of course the conclusion and we should pay most of our attention to this. However, as a brief side-note, there is an assumption going on here between the premise and the conclusion. The argument is assuming that just because it is difficult to judge how thorough to be, physicians fail to administer the right amount of thoroughness to their testing. A small assumption, sure, but something to think about regardless.
However, for the purposes of this task, there is also a really big assumption about this "feeling" that patients have. Who is to say that this "feeling" actually tells them anything? The conclusion is basically saying (Don't feel ill → Unwise to have medical checkups). However, what if the worst diseases one gets happen to be when you don't feel ill at all? This is the first thing that I was thinking about.
(A) This seems to weaken the conclusion very very slightly. If not all medical tests entail significant discomfort then maybe extra testing won't do all that much. Maybe extra testing will be perfectly fine and eliminate one major objection to receiving them. Either way, this definitely doesn't strengthen the argument.
(B) Oh this one looks good. It seems that this provides a reasoning why you shouldn't receive medical testing when you "feel" you don't need it - it is because it can make you ill! I'll keep it for now.
(C) I am unsure how this does anything to the argument and it definitely doesn't have any bearing on the conclusion. I'll eliminate this for relevance.
(D) This gives a reason why one should absolutely get extensive tests done - these complex tests make it more likely that a rare disease will be discovered! This would thus seem to weaken the conclusion.
(E) Like (C), I am really unsure about how this does anything to the conclusion.
(B) is the only one left and I think it makes the most sense (apparently, so does LSAC). (B) provides a reasoning why we can believe that we shouldn't just get checkups willy nilly. After all, they can make us ill with all their crazy testing!