He says he is is not the Doctor, but he is still her Thief, so she mourns his passing like she does all the rest. There are traces of him, like the others that have come and those that will come, in a secret room that no one else will ever see. In the room, there's a copy of a long, impossibly patterned scarf draped over an armchair that once sat in her console room. Beside it, an ever-green stalk of celery. Mementos and reminders... And there, just as prominent as the rest, a long, brown overcoat, dusted with Gallifreyan sand.
Sometimes, when she is alone, or her Thief is taking a rare nap, she'll pull his image up on the console screen. A quiet act of rebellion; of remembrance. Her Thief may like to forget him, but she never will. He made a hard choice, and he paid for it in shame and scorn. But he was hers, and she was his, just as it always will be.
The TARDIS mourns him, because no one else will.