There is really only one answer to this question; the pilot has no choice. Here's what the U.S. FAA says about it:
Sec. 91.7
Civil aircraft airworthiness.
(a) No person may operate a civil aircraft unless it is in an airworthy condition.
(b) The pilot in command of a civil aircraft is responsible for determining whether that aircraft is in condition for safe flight. The pilot in command shall discontinue the flight when unairworthy mechanical, electrical, or structural conditions occur.
Does "hitting something" equate to loss of airworthiness? I think it would be successfully argued by the FAA (in their certificate action against the pilot) that once he became aware that he'd hit something with his aircraft, he could not be certain that the aircraft was still airworthy. Therefore, he would require him to land. Further, it would be a weak argument for the pilot to state, "Well, yeah, I knew that we hit something, but I was sure it didnt cause any structural damage."