Very interesting, thank you The Royal Watcher!
The Montagu family seem to be amazingly camera shy, despite being so frequently involved in politics. Not only are photos of the Countesses and the Viscountesses Hinchingbrooke rare, it is even rarer to see them with evening jewels. Apart from the current Viscountess Hinchingbrooke, I could not find any of the ladies (or most of their daughters) wearing a tiara.
The exception is Lady Katherine Montagu, daughter of Victor Montagu, the 10th Earl who held the title from 1962 to 1964. In 1964 he disclaimed the title to ensure he could run for a seat in the House of Commons.
Although the photo below is not very clear, I think that Lady Katherine was wearing the tiara in question to her wedding in 1965.
(I have seen two spellings of the name, one is Katharine, the other is Katherine)
Detail
The tiara does not show up in any of the very few lists of wedding gifts available. In fact very little jewellery is in any of the wedding lists.
It is interesting that Julie Montagu is not the first American bride in the family, that honour goes to Alberta Sturges who in 1905 married the then George Montagu, who later became the 9th Earl.