The correct option to complete the reporting of the dialogue is "had come." This choice accurately converts the present perfect tense "have come" used by the student in the direct speech to the past perfect tense "had come" in indirect speech. The past perfect tense is used in reported speech when the reporting clause uses a past tense verb (e.g., "mentioned"). Let's see how it fits into the sentence:
The student greeted and mentioned that she had come to inquire about the English courses for international students. The administrator enquired if she was a student at the university.