Also, on the subject of her complaining.
What exactly does she plan to complain about?
She can't complain about you wearing a visible religious symbol, because she wears a hijab herself, and because yours was so discreet that she only saw it accidentally, meaning that yours is generally not visible.
So even if it were against any rules for you to wear a visible religious symbol, which, in the UK, it isn't, that can't be the basis of her complaint.
In which case, what is she planning to complain about? Which of her rights does she think have been infringed here? She doesn't have a right not to come into contact with Jewish people. She doesn't have a right to know your religion if you choose not to share that information, any more than she has the right to know a doctor or nurse's religion before they're allowed to treat her.
If the basis of her complaint is that she wouldn't have done the course if she'd known that the teacher was Jewish, your manager needs to do is point out that in this country we have freedom of religion and belief (which is why she is allowed to practise hers), that it is illegal to discriminate against people on that basis (which is why they couldn't refuse to hire a Jewish teacher even if they wanted to, which they don't), and that they have a duty to protect you, their staff member, against antisemitism. Accordingly, they can no longer have her as a student.