I didn't call the hotel. I didn't have much confidence in the frontline staff, based on conversations when I was there.
I am also lazy and the Hilton app makes it much easier to leave a comment in the feedback section than call the hotel and try to find the name of the right person to speak to, wait on hold etc.
I did however call the Diamond Desk and am happy to say that the hotel has now made the appropriate refund and communicated this to Guest Assistance/Diamond Desk. No apology or direct communication from the hotel though.
I would not have gone down the chargeback route easily though, for fear of losing my Hilton Honors account.