I struggle with exactly the same feelings. And if my T had said what yours did, I'd be devastated and feel an intruder too. Although I totally agree with what Oliva said that it's most likely your T wanting to be there for you and struggling to maintain personal boundaries. I had a situation recently where I panicked because I thought I'd intruded on my T and her life but my T made clear she'd reply when she could and if she wasn't able to say much in her reply due to lack of time, we'd always talk about it. That helps me to see that she can manage her boundaries but I can contact her when I need to. It sounds like you can do the same with your T, it's just that your T is still working on managing her boundaries and unfortunately put that struggle onto you, but you're not an intruder in her life even though I understand how much it feels like that.