I confess I haven't read that book so cannot comment beyond to say that Victoria Melita's mother and mother-in-law were both called Marie, so maybe it was a confusion between the two women by the author?

Unless of course the author has some evidence to show that Marie Pavlovna bought it from Marie Alexandrovna and gifted it to Victoria Melita, however we know that Marie Alexandrova was one of the wealthiest princesses in Europe and had no need to sell her jewels before WW1 so that would create another mystery.