I have never seen pictures of Queen Elizabeth (later the Queen Mother) wearing this diadem. Maybe that she considered that her own crown (in the circlet version, without the arches) was enough for her?
In The Queen's Diamonds (2012), Hugh Roberts mentions, in the chapter dedicated to the Diamond Diadem, that "small alterations" were made for Queen Victoria in 1838, for Queen Alexandra in 1902 and for Queen Elizabeth in 1937.
Maybe that Queen Elizabeth wore the Diadem in one of the ceremonial occasions organized at the time of the Coronation? Or it could just be that, as a Crown heirloom, the Diadem was cleaned and repaired a few months after Queen Mary handed it over to the new Queen, without necessarily implying that the new Queen ever wore it.