Is it because of guilt or pride that you're not comfortable with such a low fee?
Like others have said, she wouldn't have offered if she couldn't afford it.
What is the alternative? Not seeing her? Wouldn't that be worse?

But I also totally understand that you don't feel comfortable.

Personally, I'm too proud to ever accept something like that. Some months ago, I was in a tight spot and my T told me that she was fine with me not paying her for a few months. I refused because I'm proud and also didn't want to owe her anything, I wanted to stay in control (somewhat).