Regardless of how your T feels about payment, I think this is worth working through. My T offers email and phone contact between sessions for free, and my guilt/worry about reaching out was huge and astonishingly tenacious. It has taken years to get to where I can reach out and expect that she won't get angry at me for being "needy." (I'm still not perfect at it.)

I was doing the same thing with her that I was doing with other people, being unable to express my distress or ask for support if the other person wasn't being compensated or paid back in some way. It was keeping me isolated and stuck. Working through that in therapy has helped me be more comfortable and connected in the rest of my life. Obviously therapists are a bit different from friends in that it is a paid relationship, so I think it's fine to talk about how your therapist feels about paid outside contact. But I do think there could be some rich material around your anxiety about reaching out. It could be a missed opportunity if you side-step the whole emotional issue by using payment to assuage your guilt.