I have told my T this. All of it, even.

She stopped taking my insurance 6 months after I started seeing her. She knew I couldn't afford to see her at the cash rate, so she offered to let me to pay her the rate my insurance had been paying her (total value, not just my copay). I gratefully accepted.

A year after I started seeing her, I took 3 months off work on short term disability to do ECT, among other things. STD only paid me about 25% of my usual paycheque, so I told her I'd be down to seeing her once a month while I was off work. She was not okay with that, wanted to keep me at 1x/week so she dropped her fee entirely.

We talked about it a lot because it made me incredibly uncomfortable. Eventually, though, I had to admit that a) she, unlike most people, had the training to put thought into the offer and wouldn't have made it if she weren't okay with it and b) it was possible she could care about me even if I didn't pay her.

Option a) is what really got me through it. Occasionally since then she has comp'd a session or I've forgotten a cheque and it tends to wrack me with guilt. Then we talk about why it's so hard for me to believe that someone might care for me.