Please tell me the confirmation number you got when you made the reservation.
Literal
Reservation-of occasion-[at-に] heard confirmation-number [object-を] me [to-に] tell-[polite-てください].
Relative clauses again: 予約の際に聞いた modifies 確認番号 — 'the confirmation number (that was) heard at the time of the reservation.' 際 (さい) is a formal word for 'occasion, time, juncture' — common in written register, rarer in casual speech. The past-tense 聞いた directly in front of 確認番号 does all the work that English handles with 'that you got.'