presumably you have code that uses millis() to update the display after some interval and keeps track of the next phrase to display.
and you want to add code that checks a button changes the mode.
the button press can be used to change a "mode" state variable which is used to loop() to determine what to do which can be to call a sub-function to update the display or do something else, call some other sub-function. this can be done in a switch statement in loop()
so loop calls a function to check for button pressed and uses a "mode" variable set in the button routine to decide what to do