Explanation

Creating a filter: the original sentence has problems near the phrase "be made extinct." As written, the sentence fails to convey the intended meaning. The meaning as written might indicate that the species is made extinct on a regular basis, whereas, in fact, it's something that has happened and completed. The meaning could be expressed properly as, "a species most observers agree to have been made extinct." So (A) is out. We'll look for a simple past tense instead of the infinite "to be."

Applying the filter: choice (B) has a defect: "that" is misplaced in coming after "most observers agree." If we use the word "that," we introduce a clause, and there is no verb for this clause. So (B) is out. Choice (C) uses "that" in a in a valid clause. The words "humans' hunting" is a little awkward, but it's grammatically correct. We can come back to (C). Choices (D) and (E) both have problems. In (D), the observers are not quite agreeing on the right thing. The intended meaning is that they agree on the fact and method of extinction, not the identification of species. Choice (E) also has that problem. In (D), the word "as" is not proper usage to equate "species" logically whether the thylacine. In (E), the infinitive "to be" has the same problems identified in (A). So (D) and (E) are out. The correct answer is (C).