On 3 June 1913 the Times carried a report that Sir Charles Wakefield, a wealthy philanthropist and later Lord Mayor of the City of London, had authorised a bust to be carved of Queen Mary by the famed sculptor, Sir George Frampton. It was to be presented to the Guildhall.
The Guildhall site has an excellent zoom in feature which allows us to see that Queen Mary is wearing the diamond and pearl choker we are all familiar with.
Below is another image of this sculpture. It is by Stephencdickenson who has placed it on the Wikimedia Commons site.
By Stephencdickson (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
As the Queen would have known that the bust was for the Guildhall I suspect HM chose to be depicted with this jewel as an acknowledgement of the City's gift to her.
One thesis notes that the members of the royal family always did sittings for Frampton, and so I doubt if the choice of jewels depicted was left to the artist. See http://etheses.whiterose.ac.uk/303/1/uk_bl_ethos_399910_vol1.pdf page 293 - the comment is next to the listing for the bust of King George V. On page 196 the author states that the bust was presented directly to the Guildhall but did not (for my purposes) have the crucial link that it was commissioned for the Guildhall.
I believe that the diamond and pearl choker Queen Mary has been photographed wearing on grand occasions is the wedding gift from the City of London, although I accept that perhaps only Queen Mary's jewel inventories will provide conclusive proof.