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May 23 seems an odd cut-off date. I can tell you that a few days before May 23, I booked a hotel stay for the end of the year with the Citi Concierge and it is covered under the 4th Night Free benefit according to the confirmation email. It's a boutique hotel, so not usually part of online travel booking portfolio. I recommend calling again and trying a different rep.
Did you call more than once and get the same answer? I have the feeling you just got a misinformed or lazy employee who didn't feel like doing her job. According to Citi's memo, you should be able to book through concierge till the end of August. I used the benefit at the end of last month through concierge.
The booking process can take a little while. They have to get you registered if first time user. Then, they search for your dates to confirm availability. After that, they have to put you on hold while they contact the hotel directly to make the reservation and give them your loyalty info. Finally, you get a confirmation email with your booking details.
Just in case, when you book through concierge, you have to pay the full amount of the stay including the 4NF. Citi will refund the 4th night within the next 2 statements approx. If you book on the TY site, the discount is applied at the time of booking.