A gerund is a verb functioning as a noun. In this case, the gerund is "band-aid" and it is the direct object of the sentence, where "on the cut" is the phrase of the indirect object, which is the "cut". Hope this helps!
I believe the answer is C because if you looking for dog pictures and end up looking at cat pictures you went off topic, since you went to look at dog pictures. Its the same when you go looking for research on a topic.