I fixed his links so you can see them now. My friend who worked for years in the Christies Russian Department in NYC said the crown was Princely one, not the Imperial. Also, there is no cypher of AH for Anastasia Nicholaievna and in all of the formal photos of the Grand Duchesses, none of their gloves has a visible crown embroidered on them. The choice of colors is also most atypical of the era, when the monogram would have been in the same color as the leather and in an unobtrusive place, either inside the gloves or on the inside near the cuff.
There is an old story written by an English woman who was invited to sit in the Imperial Box at the Mariinsky Theatre, with the Grand Duchesses, during a performance. She recalled how Anastatsia, who was a child at the time, came in with a full box of silver foil wrapped chocolates, and during the performance at the whole box with her gloves on and got chocolate all over her leather gloves.
We get literally hundreds of people a year who claim they own something of the Imperial Family, given years ago by somebody Russian, and so far, all but one of these claims has been a made up story lost in family lore. The Christies expert doubts the story highly.