The tiara was part of a parure that Bertie gave to Alix as a wedding present. It consisted of the tiara, a necklace, earrings and a brooch. It was those jewels she wore on their wedding day. (There is a photo of the complete parure on page 3 in "Queen Maud of Norways wardrobe").
I think it is very unlikely that her children would split up the parure after Alix's death, and there is a photo of Queen Mary wearing the brooch in 1938. So I think the tiara and the rest of the parure was given to George and Mary. The necklace and the brooch was owned by the queen mother until her death. Since Elizabeth by then already owned the earrings, she probaly inherited the necklace, brooch and the tiara. (She has only been seen wearing the brooch once, back in 1972 on a state visit to France).
Of course, this is only my guess. But I think it's very easy to imagine that Bertie and Alix's children felt, that their father's wedding present to their mother, should remain in the reigning monarch's family.