I sent them the screenshot, but they still insist this fee is not waived on points stays. Honestly, I don't know how it could be any clearer that this fee should be waived.

The Hilton Terms and Conditions (https://www.hilton.com/en/hilton-hon.../#reward-stays) clearly state that "No resort fees on Reward Stays booked using all Points, or for Promotional free night stays (e.g., issued by credit card partners, etc.)." And, this charge is listed on the hotel's own website as a "Resort Fee."