You might also want to try simply overwriting the old lines and then drawing the new lines. Like this:
SCREEN 12
LINE (MAZE)-(LINES),RED,B
LINE (MAZE)-(LINES),RED,B
LINE (MAZE)-(LINES),RED,B
[user/computer movement command entered]
LINE (MAZE)-(LINES),BLACK,B
LINE (MAZE)-(LINES),BLACK,B...