Our memory can only remember so much in an hour so it's important to write down the points you want to take with you. Taking notes will ensure you take full advantage of your tutoring session.
There are many ways of taking notes. Try different methods until you find one that works best for you. No matter which method you chose, a universal tip is to hand write the notes whenever possible. Hand writing notes helps to remember them.
Here's one note taking method:
Ask yourself, why am I meeting a tutor today and what do I want to know more about (example: I'm struggling in Calculus and want to learn more about integration). Write this on top of a sheet of paper. Throughout the lesson, refer to your answer as you take notes. This method ensures that you don't write down everything the tutor says, but instead only the important ideas that relate to the topic you want to know more about. The best notes are concise, as quality matters more than quantity.
Also, Top Tier Learning tutors do not think it's rude to take notes and actually encourage it. We enjoy seeing students take interest and as a result, thrive in their classes.