Client does not want me to record

I have a client who I’ve coached for 2 sessions. She wrote this to me: “There’s a feeling of significant unease that I felt at the time and that’s persisted, so I have to request you delete this recording and any copies of it. I shared what is very personal and private information for me, so I feel very uncomfortable there’s a recording of it. Also we’ve only just met and trust is still developing.” I get this somewhat, although the recording is automatic for my Zoom account and I confirmed with her it’s simply for my notes. She also said that she wants to record it and, if I want notes, she will send me her notes.

C – Client wrote the above
T – If she won’t allow me to record, then I won’t allow her to record – I need to cancel her as a client.
F – Untrusted
A – Consider telling her that there seems to be distrust and so not a good fit, don’t allow myself to consider where she’s coming from and teach her what her brain is doing, stew about it, feel bad that I haven’t caused her to feel trust (I know I’m getting into her model), consider simply refunding her the money minus the sessions we’ve had.
R – Haven’t decided what to do, but her call is coming up in 5 minutes.

My game plan is to explore this with her, allow her to record and me to not record, simply work through the remainder of her sessions like this. Then have a plan for any new clients and set the expectation up front.

Any other suggestions?