This thread is getting heated and I don't necessarily agree with some things on here but here's my opinion.
I'd say no, there's no need to tell her because like some other people have said, unless you are very close to someone or feel comfortable, there is no reason to disclose information you don't feel like sharing.
For example, I'm straight but I don't think I'm entitled to tell people that?
Let's say I'm talking to a guy and he gets the feels for me. Just because I'm straight but talk to them a lot doesn't mean I'm leading them on! What kind of ridiculous nonsense is that? It's not my fault he fell for me, just because I'm straight doesn't mean that I have to have feelings for someone who is of the opposite sex.
So from my view, no, you don't need to tell them because you have done nothing wrong! And you are an amazing person and do not owe anyone anything. If her mistaking you as a cis guy makes you happy, then go for it!
Unless you explicitly said you were born a male and lied, I don't think there is anything wrong with it - and even if you did, you and your safety and happiness come first. It is perfectly possible she was looking for a friend as myself - who lacks friends - also does that same and no, I don't just catch feelings with a random guy who I talk to over the phone just because they're nice!