Disclaimer: I have never used the online Check-in, so not authoritative.
Whenever I have booked direct with TG, either on phone, or award redemption, on the e-ticket, there is a line which says 'Booking Reference for Kiosk/Internet Check-in'.
This code is not the Amadeus booking code, but the code from TG's system.
Haven't seen that particular line when tickets are booked and issued online or booked /issued by Travel Agents. Haven't seen them either on tickets booked online but issued at TG city offices.
So, I would think that the TG code is what you can use to check-in online.
YMMV, as always.
Cheers!