During her reign, we saw the sale of several Jewels, including many important Royal Heirlooms, from the Queen Mother (probably Queen Mary's Amethyst Tiara and Parure), Princess Margaret (probably the Cartier Diamond Lozenge Bandeau and many important heirlooms at the 2006 auction), Princess Mary, Countess of Harewood (Queen Victoria's Sapphire Coronet and Parure among many others), the Kents (the Cambridge Sapphire Parure among many others), and Gloucesters, as well as pieces like Queen Victoria's Turkish Diamond Necklace by the Duke of Fife.

The only reason I can think of Princess Margaret not selling the Cartier Diamond Lozenge Bandeau more publicly and in the US would be to save a bit of face and not advertise her financial troubles to the world.