Are points taken back when an order is refunded or canceled?

Yes. In the "Place an order" earning rule, turn on "Deduct points when an order is cancelled, or fully or partially refunded". Points are deducted automatically, also for partial refunds. For example, if a customer earned 100 points for a $100 order and returns half of it, 50 points are deducted.

Learn more: Automatically deduct points on refunded or canceled orders · Earning rule – Place an order