Why? Kitty Howard's been raised in a lax atmosphere where such things were considered "normal". Kristina has already been married (to someone that even Karl V was concerned about his sanity) and widowed. She's a princess of Denmark, with an Austrian archduchess for a mother and an emperor for an uncle. She's not gonna act like some provincial skank seeing the big city lights, whose dad is a younger son of a family that as they would've said at Versailles (like they did of Marie Lesczynska): "they do not even know who the grandparents are" (implying a parvenu). Kristina knows very well who she's descended from: Trastamara, Valois, Habsburg and Oldenburg (all dynasties older than the Tudors).
What would be his grounds for divorce? If it's adultery see above. Anne of Cleves never slept around so why would Kristina? And if he WERE to behead her, he'd unleash holy hell from all sides. The Habsburgs, Oldenburgs and Stewarts, because she was related to them; the pope would declare Henry deposed in favour of Mary. Which means the French might get involved since they might want a Valois/Stewart prince to wed her just to stop another crown being added to the Habsburg collection. And its not like Henry can rely on the Protestants, since as Mary said when they brought her news of the king's marriage to Anne of Cleves "I do not know what to make of the king. He burns one Lutheran and then marries another"
Her paternal grandmother was also a Wettin, she was pretty much closely related to everyone who mattered in in continental politics.