When you have to communicate with the parent scene, a nice approach is to use signals.
So you can have a script in your Panel that basically exposes signals this way (partial code):
signal choice1_selected
signal choice2_selected
func _on_Button1_pressed():
emit_signal("choice1_selected")
close()
func _on_Button2_pressed():
emit_signal("choice2_selected")
close()
Then in the scene that contains this panel, you can listen to those signals by connecting a function to them.
You could connect directly to the buttons, but it's as wrong as accessing private members of a class IMO, and it would break if you change or rename the buttons later.