You might ask the registration office about their relationship with Airbnb. Many hosts use more than one website for finding guests, but if you only use Airbnb, you may be exempt from the payment. Most cities require licensing, but the ones with a relationship with Airbnb should not be double charging the licensee. My city tells me to report the number of bookings from all websites I use every 3 months, but to NOT add Airbnb bookings to my tax form at the end of the year when taxes are due. This prevents me from having to double pay those taxes.
Since airbnb has the deal with your city, they would be obligated to make the payment, so I seriously doubt that they would release the taxes to you.