Symbolism, Imagery, Allegory
A bloodstained handkerchief probably isn't on your list of dream graduation gifts, and yet this is exactly what Ani's mom gives her when she sends her off to Bayern: a handkerchief speckled with her own blood. Gee thanks, Mom.
Before you get too squeamish, though, consider this: the handkerchief—"made from a thin ivory cloth with green rust, and yellow lace edging" (3.24)—is a family heirloom, passed down from Ani's grandmother to her mother. So when her mom gives Ani this piece of cloth, she is sending her off to Bayern with something that symbolically links her to her family and its history.
Not only is this something passed down through the family, but it's something Ani's mom cares a great deal about. She used to carry it around herself, and when she presents it to Ani, "the queen pulled a neatly folded handkerchief from her sleeve and smoothed it open" (3.24)—that it is folded neatly and she runs her hand over it both show regard for the object she is presenting. And because of this—because this is something with sentimental value to the queen—it symbolizes her love for Ani.
As for the blood, it's there to protect Ani—it's supposed to keep her safe, in a magical sort of way. So instead of being gross (although we maintain that a bloodstained handkerchief is still a pretty gross present), the blood is a symbol of both protection and her mother's concern for her safety. And when Ani loses it, well, it clues us into the fact that all bets are officially off when it comes to our main girl and her safety going forward.