Phoenix.Fourtysix is correct and should not have been rated down.
From ffxiclopedia:
Speak with the Tarutaru Sutarara, who will talk about the Tenshodo, and about it being "right under your nose". Ghebi Damomohe is at the counter. Speak to Ghebi and select the third, blank line of dialogue. Ghebi will say that you need either a Tenshodo Invite or a Tenshodo Application Form.
Either:
Head to Port Bastok and into Warehouse #2 across from the Airship Agency. Once inside, talk to (Jabbar) to receive the Tenshodo Application Form, then head back to Ghebi Damomohe in Neptune's Spire. Giving Ghebi Damomohe the Tenshodo Application Form grants you a Tenshodo Invite and completes the quest.
Or:
Buy/trade for a Tenshodo Invite. Return to Ghebi Damomohe in Neptune's Spire. Giving Ghebi Damomohe the Tenshodo Invite grants you a second Tenshodo Invite and completes the quest.
Notes:
You may need certain fame or reputation to start this quest
It's helpful to know that you do get a NEW invite from the NPC after trading her one to finish the quest for Tenshodo Membership. Meaning, if you don't have enough fame for the quest (or simply don't feel like traveling to Bastok) you can buy one of these on the AH, trade it to the NPC, and then turn right around and sell the new Tenshodo invite back to the AH. On Odin at least, you can sell it back in a matter of hours. Of course, if you decide to follow the quest instead of buying it, you can sell the new invite for direct profit. :)
you need fame 3 in jeuno to start the quest to optain this item.
when you just buy an invite from ah you dont need any fame and get a new invite back after you traded your one.
Required to get access to whitegate also. For a mule you -do not- need to get fame to enter neptune spire to start the quest, simply buy an invite off the AH to trade to Ghebi.