Probably depends on how much you value your time. On one hand, the Honors terms & conditions state "At hotels with resort fees, members on reward stays booked using all Points, or using a Promotional free night reward (e.g., issued by credit card partners, etc.) will not pay resort fees". On the other hand, the hotel has 1) shamelessly made a thinly-veiled, but overt effort to brand this as not a "resort fee" and 2) disclosed as much up front on their site.

So while they're obviously completely sidestepping the intent of the program language, they probably have no qualms about it. Question is whether they will roll over or Hilton has any appetite to make them do so.

I'd say a note to the Ambassador here on FT and an email to any manager whose email you can find (check the hotel responses to poor TA reviews and you can likely find one) would be a fair initial investment for the dollar amount involved.