Mog station says:

Aetheryte Pendulum

Teleport to the aetheryte closest to New Adventurers on your friend list free of charge.
* The Aetheryte Pendulum can be used for any New Adventurers on your friend list, even if you have not invited them via the Recruit a Friend campaign.

Check which aetheryte is closest, and see if it appears free of charge in your teleport menu. If not, check your gil then try teleporting anyway, and see if you actually paid the cost or not.