Having believed that Stephen Gardiner was indeed the son of Helen Tudor for many years, I posted his lineage on FB Descendants of John of Gaunt only to be told by many sources that he is not, referencing as the most authoritative source Douglas Richardson of whom I had no knowledge but reseraching him I find to be quite trustworthy. Even without that it was never documented that her husband William was his father, also being listed as William's brother John, her second husband, and still another John was also suggested. Your tree with the wives of his son George, grandson George and g grandson Lionel are also supposedly wrong in my lineage referencing this tree as the source. Just FYI that this tree also has errors. There are other sources and references posted in the John of Gaunt FB page
Not seeing a person in a tree, is not necessarily a proof they are not descendants. My family tree on my father's side has been pretty thoroughly documented for 105 years. And yet just last year a fellow showed up with a record of a 3rd wife, with documents that nobody had every before found.
Sure wish the absence was a definitive proof. But you can't prove a negative.