On the TV show, they haven't explained just how dangerous the Poles were as rivals to the Tudors. The family tree is all very involved but basically, Richard de la Pole and his brother were the nephews of Richard III and so Henry VII had stolen their very valid claim to the throne. They were the people Henry VIII was most afraid of in the world.
Stressed: Henry Courtenay is another branch of the York family. His mother and Richard de la Pole's mother were sisters and so Courtenay became the Yorkist claimant later on.
His son, Edward Courtenay, spent years and years in prison as Henry VIII was too scared to ever release him. His mother was great friends with Mary I and she released him - he was considered as a husband for her at one point. When Mary ddn't marry him, he tried for Elizabeth and that match was considered as a replacement for the unpopular Mary and Philip.
After an attempted rebellion, he was exiled.
(I'm a History student and Tudors nutball )