In each interaction with the hotel, as soon as I started reading that they cut me off to say that number has no meaning to us... again, this is just one hotel, Hilton Garden Inn, but .... the front desk (nor Hilton central reservations line) were able to do anything with it. And you are correct, it seems to be the Cap1 Travel Confirmation , minus the "H-"

Anyway, I've seen a lot of positive / no issue annecdotes out there, but as I've rarely done OTA bookings before (except for FHR through Amex, which I usually get an email from the hotel concierge) , I intend to call the properties directly now each time to confirm if I do this again.