According to the information given by Christie's the pearls were mounted into the necklace in 1849 for the wedding of Elizabeth's grandson, George Sutherland Leveson-Gower (later 3rd Duke of Sutherland) to Anne Hay-McKenzie on 20 June 1849.
See this PDF by Christie's https://www.christies.com/presscenter/pdf/09282007/104419.pdf
Christie's did not divulge which branch of the family was selling the necklace.
Anne Hay-McKenzie was the heir to the Cromartie titles which had been forfeited by an ancestor after the Jacobite rising in 1745.
In 1861 the titles were recreated for Anne. To ensure that the titles were kept separate from the Sutherland title, the grant provided for the Cromartie titles to go to her second surviving son, Lord Francis Levson-Gower. Failing male heirs the title could pass to female descendants.
As the necklace was later worn by subsequent Countesses of Cromartie, it would appear that the jewel was not entailed to the Dukedom of Sutherland. Presumably, it had been a personal gift to Anne Hay-McKenzie, later Duchess of Sutherland and 1st Countess of Cromartie in her own right and she probably left it to her second son or his wife.
Francis, 2nd Earl of Cromartie, had only 2 daughters so the next holder of the title was his eldest daughter, Sibell, 3rd Countess of Cromartie, who gained the title in 1895.
There are very few photos showing Sibell, Countess of Cromartie, with grand jewels.
For the coronation in 1902 she wore only a modest string of pearls and did not wear a tiara.
I suspect that the necklace was then in the possession of her mother as a personal jewel, as for the coronation in 1937, Sibell wore the necklace as a tiara.
Sibell's son, Roderick, married twice. His second wife, Olga, wore the necklace for her wedding in 1947
and the press reported that Sibell, Countess of Cromartie had given it to Olga as a gift.
Roderick, the 4th Earl was succeeded by his son, John, as the 5th Earl of Cromartie. His second wife, Lilias, was photographed wearing the necklace. She died in 2013.
For her obituary see https://www.scotsman.com/news/obituaries/obituary-lilias-countess-of-cromartie-1-3147215
So from the time Anne Hay-McKenzie died in 1888, and perhaps even earlier, the necklace was with her descendants in the Cromartie line.
I found numerous press reports at various times stating that the pearls had been given to Lady Sutherland by Marie Antoinette,
(For example this one from 1953)
and stories of the friendship between Marie Antoinette and Lady Sutherland.
Although the necklace failed to sell at auction in 2007 it is likely to have been sold privately afterwards.