How do I create a bitmap from the screen in MFC?

I'm creating a version of Othello (Reversi) for my Programming and Algorithm Design class using MFC. I currently am drawing transparent bitmaps over the squares containing legal moves, but I have yet to find a way to make the boxes disappear when it is the next person's turn without redrawing the entire board (which causes the screen to flicker). Does anyone have any suggestions on how I could make the red boxes disappear so that the board is visible under them?

Thanks in advance!
Rachel