Right off the bat, I can think of one way to do this.
In Photoshop, make your grid visible:
View --> Show --> Grid
Set your grid setting to something small in Preferences:
Preferences--> Guides, Grid, Slices, & Count... --> Grid: Gridline every: 10 pixels(or whatever)
Set "snap to grid":
View --> Snap , and then make sure that in "Snap to" that "Grid" is selected.
in your image, use the rectangular marquee tool to cut out the desired area(the quadrant of the "O" in your image above) and then use the same marquee tool to select and fill individual squares with the same color. The marquee should snap nicely to the confines of the grid sectors, insuring an aligned pixel look when you're done.
Well, that's one way, anyway.
Kurt