I am aiming to change the a part of the Tkinter screen when a button is clicked.  Do I have to destroy the screen then redraw it (to create the illusion that only a part is being changed?) Or can I keep the button there and somehow only change one part (like the graphics.) Thanks!
No, you do not have to destroy the screen and redraw it. You can easily insert widgets into the current window when a button is clicked. There's nothing special about being run from a button click -- the code is the same as your initialization code.
Changing Tkinter Screen when button is clicked?