agreed Henry totally flips his shit, though in 1534-36 Anne Boleyn is still Queen, she was executed 19 May 1536, Jane Seymour marries the King 11 days latter, and gives birth to Edward VI 12 October 1537, Mary leaving had a lot to do with fear of what Anne Boleyn might do to her to protect Elizabeth's place, so how does Henry see Mary leaving, does it make him think he needs to double down the the Church issue and on his Marriage or that the need for a male heir to use against Mary is needed at once, I think it matters a lot when she leaves, before the death of Catherine of Aragon (8 January 1536) and the King starting his afar with Jane Seymour, before that point likely the former, while Henry's relationship with Anne was falling apart and it was becoming clear she wouldn't have a son, he was still unwilling to throw her over while Catherine lived, with-in months of her death Anne was out.
so Mary leaves before her mother dies, Henry doubles down, Anne might get knocked up and maybe this child is a live Prince, maybe she was just doomed as some historians think, whatever, likely Elizabeth is made (formally) Princess of Wales and set up there, Mary looses all titles and Henry never allows any one to speak of her again, she dies in court far from England and is all but forgotten to history
Mary leaves after Catherine's Death, Anne's fall starts nearly at once, the King Rushes to marry Jane, and she is knocked up nearly at once, maybe with a quicker TL she makes it through ok, or maybe she dies birthing a daughter this time, Elizabeth, always more disliked by Henry then Mary is even more disinherited then OTL, Henry never risks putting her in line or revoking her bastardy because ether move would put Mary's place in question, the Grays are heirs, maybe in TTL some of them are even men this time, who can say what might happen with Henry and Jane's children and its clear Henry never had any others (despite being married to a young horny girl and his last wife was knocked up nearly at once in her last marriage) so maybe there's no one left, or maybe Henry FitzRoy lives in TTL and is heir because he's male