Yeah you can request for the refund of your right of PR fees as you did not exercise your rights of being a PR. I will suggest you do that right way if you have not done yet. Also check if it has been refunded already to your credit/debit card account you used for paying. As of now, I would suggest you only pay the processing fees while you submit a request for the right of PR refund. But if you do not get a refund and if they ask you to pay right of PR fees, I would suggest you pay it while waiting/asking for the refund, as there might be delays on the refund.
Edit: Do attach your previous receipt with barcode confirming payment in your request for refund, also attach that receipt indicating no refund has been made while submitting your new application.