I believe she was a member of the Magisterium.
The story that was told to Quentin said that Andross accused them of stealing it. Andross informed Kip that he knew she had taken it. Maybe she stole it from Andross and either was caught by Gavin, or tried to get Gavin's protection (thinking maybe that being the prism he wasn't corrupt). Regardless, Gavin "humbled" the strong woman.
the Luxiats of the Magisterium aren't drafters.
From his blinding, we know that Gavin (Dazen) can definitely call up black. I'm assuming he probably can call up white as well, though he doesn't know he can (or know how).
We all assume Gavin will break out of the prison. Perhaps he will be rescued from it? Teia has the master cloak. The Order doesn't know she has it. I think that knowledge will make Teia a powerful enemy of the Order.
There appears to be a few players that knew about Lina. Garadul obviously did... Though to what extent we don't know. He was the son of the sataraph of Tyrea, and later the king. General/Sataraph Danavis knew about her and who Kip was. Andross knew who she was. Grinwoody appears to know (as to at what level, slave or master who can tell).
Dazen was clueless to the whole thing.
I remember the man Teia killed saying "goddess" but at the time I didn't take it the same way you did. If you remember when Kip killed Vox (or rather Vox killed himself) he was crying for Atirat to come back. Perhaps this man was calling to the Ultraviolet goddess Ferrilux?