My friend and I both had a similar situation in grad school. Both of our parents hassled us about it. My friend decided that she'd rather take on (significant) debt than deal with her parents. That worked for her.

I took a different approach. I ended up having a joint checking with my mom so that she could deposit money for me to write checks to my T. She griped about it, but I felt therapy was essential and I didn't want to take on the debt. Eventually, I was able to let my parents' comments about my therapist's greediness, ineffectiveness, etc. roll off my back. Honestly, my mom will still make the occasional comment about that "terrible T" I had in grad school (it has been over 5 yrs since I saw her).

Talk to your T about this, your relationship with your parents, and what would be best for your mental and financial health.

Good luck!
EJ