When we previously used the certificate(s) from the Citi card, we were advised to take a printout of the certificate (email) showing the Certificate ID and provide it to the property. Since a certificate stay is still considered a reward stay, that printout allowed the property to verify that the stay should be fulfilled via the certificate and not via points.
I do not see anything in the Ts & Cs to *require* that extra step, so I'm guessing there must be a shortcoming in the reservations / fulfillment system that makes the procedure a "best practice" rather than a requirement. And you may have been caught up in that shortcoming.

When you say that you no longer have the cert, do you mean you no longer have the email with the ID? Have you tried calling Citi to see if they have a record of the Cert ID that was issued to you? That may allow HH to match it up after-the-fact, and/or show that the Cert ID has been used. (and when?)

Looking back at the reservation confirmation email when we used the certs, the email specifies the number of points that would have been charged if it was purely a points redemption, with no mention of the certificate(s), so it doesn't appear that would help you in this case. I remember that made me nervous at the time, but I was assured it was linked although again advised to take a printout.

To gengar's point, I do not remember what the stay looked like after-the-fact, and it has timed out from the history so I cannot view it now. Perhaps a subsequent reader can look at their more-recent redemption and report back. But I certainly agree that the display could be more clear and allow better tracking!