The correct answer is: D. No improvement
The sentence "We were not the wiser for all this effort to explain the case to us" is grammatically correct and conveys the intended meaning effectively. The word "wiser" means "having more knowledge or experience." The sentence is saying that the speaker and the other people who were listening to the explanation did not learn anything new from it.
The other options are not as good as the original sentence. Option A, "none," is grammatically incorrect. Option B, "neither," does not make sense in the context of the sentence. Option C, "nevertheless," could be used to add a contrast to the sentence, but it is not necessary in this case.
Therefore, the correct answer is "No improvement."
