They keep saying "Come here, let me see your face." and "Haven't seen him around before." and there's also a guy by the door whom I can't just bypass. How do I do this?
Those words just depend on your race. If you're a High Elf, go out the door to the guard and tell him Elewen needs him. But I know you aren't a High Elf because of the way the Thalmor soldiers say it.
Here are the dialogues of Thalmor depending on race.
High Elf: Must be new around here.
Wood Elf: Seems a bit short to me.
Human/Dark Elf/Orc: You there. I don't think I've seen you around before." or "Come here. Let me see your face." or "Haven't seen him/her around before." or "Must be new around here [This must be one of the races you're using].
Beast [Khajiit or Argonian]: Wait, is that a tail?
If you're an Altmer, you can tell the Wizard at the door to talk to Elenwen. You must use Speech. If you fail, the courtyard will be hostile.