Purchase a World Pass to unlock the invitation feature of the Gate.
The bonus for the invitation feature depends on the type of World Pass purchased.

30-Day World Pass Bonus:
This lets you invite a character to your MYSEKAI, guaranteeing that they will visit every day for 3 days.
You can also earn 1 extra Memoria from that character each day.

1-Day World Pass Bonus:
This lets you invite a character to your MYSEKAI, guaranteeing that they will visit on the day the pass is activated.

The invitation feature is hidden unless you have an active World Pass.

*If you uninvite a character, they will remain in your MYSEKAI until 5 AM (PT) the next day, at which point their invitation will expire.
*If you change your Gate to a different group's Gate while a character has an invitation, that character will leave your MYSEKAI and their invitation will expire.
*After the Pass expires, your current invitation will remain in effect until 5 AM (PT) the next day.
*If you re-purchase a World Pass after it expires with an invitation in effect, the details of that invitation will be carried over, including the time limit before changing invitees.
*If your Pass expires and less than three days have passed since you last changed your invitee, you may not be able to invite a different character immediately after purchasing a World Pass.