I would think that not only would T's part of the conversation be altered by recording, your end might change too (and there is really no way to record without either of you knowing!)

I think that secretly recording has the huge possibility of blowing up on you. I think if T finds out, it is likely to end in an ugly rupture that may or may not be possible to repair. Whether it is right or wrong, I could see a T terminating a client for this. For example, they might become paranoid that you are trying to gather evidence to sue them. Maybe it is theoretically possible to hide it from them, but don't you think you might be tempted to say, "When I was listening to the tape of our session..." Or call them out on something they said that was contradictory and show them the evidence that you were right? I know I would be tempted.

If you want to gain more "factual" stuff from the taping, maybe note-taking would be a better option. If you want her voice, maybe you could just ask her to send you a positive voice mail that you could save.

Best,
EJ