A website called Women on 20s addresses the question of removing Jackson this way:
WHY BOOT ANDREW JACKSON FROM THE $20?Okay, that's a valid criticism that I've shared here more than once.
TWO REASONS THAT ARE GAINING TRACTION:
1. Andrew Jackson was celebrated for his military prowess, for founding the Democratic party and for his simpatico with the common man. But as the seventh president of the United States, he also helped gain Congressional passage of the "Indian Removal Act of 1830" that drove Native American tribes of the Southeastern United States off their resource-rich land and into Oklahoma to make room for white European settlers. Commonly known as the Trail of Tears, the mass relocation of Indians resulted in the deaths of thousands from exposure, disease and starvation during the westward migration. Not okay.
2. Some argue that because Jackson was a fierce opponent of the central banking system and favored gold and silver coin or "hard money" over paper currency, he is an ironic choice for immortalization on our money."Some" in this case are badly mistaken. The Bank of the United States in Jackson's time did not function like central banks of today. It functioned as a key institution by the wealthy to maintain a concentration of wealth and power, including direct (but legal!) bribes to Members of Congress.
But Jackson's immense contributions to democracy and his faults, especially on the Indian Removal Act, are well established in history. His reputation doesn't need a $20 bill.