My therapist thinks I’m anorexic but I’m just poor.

For context, I (F) have a salaried job and I rent. I live alone in a major unaffordable city. If I lost my job, I’d be homeless. I don’t have much savings. I can get by, but barely. I keep my expenses as low as possible. One of those expenses is food. I’ve never been a foodie. I eat when I’m hungry and I don’t give it much thought. Lately I’ve been seeing how much I can save if I significantly cut down my grocery bill. I just buy the bare minimum to not die like coffee beans stock rice bread and some vegetables. I’ve always been thin but I’ve gotten noticeably thinner. My therapist thinks I’m developing an ED but I’m too embarrassed to admit that I’m just too poor to eat like a normal person. And before you ask, I’ve chosen not to have roommates due to trust/safety issues so I’ve accepted the reality of living alone on a single income. But I don’t want her to know all of that. So I just nod and agree. She gives me tips on how to eat. What to eat. How to cope. She’s even considering treatment. I’m not sure how to tell her.