What is the value of a 1922 silver Peace dollar if it has a strange A mint mark?

That's not a mint mark on the obverse. It's the monogram of the coin's designer, Anthony de Francisci. Look closely and you'll see an intertwined A and F. Peace dollars issued at San Francisco and Denver all have their mint marks located on the coin's reverse, just above the eagle's tail feathers and underneath the Word ONE. Coins struck at Philadelphia do not have a mint mark.