The correct phrase to complete the reported dialogue is "had come." This selection correctly changes the present perfect tense "have come" (used by the student in direct speech) to the past perfect tense "had come" in indirect speech. Reported speech uses the past perfect tense when the reporting verb is in the past tense (e.g., "mentioned"). Here's how it works:
The student greeted and mentioned that she had come to ask about the English courses for international students. The administrator then asked if she was a university student.