The photo is very small. If you could post a bigger one, or if you could give your best guess of what those symbols are (they look like interlocking letters), that would help. Also, anything you know about Alfred (profession, religion, veteran status).
It appears to be two five pointed stars in the upper left and right corners. The upper center could be a butterfly or a small skull and crossbones or even crossed tennis rackets -- can't tell. The better part of the marker looks to be an interlocking capital "G" or "C" overlaying a capital "R" -- that's my best guess. My first thought was maybe "Grand Army of the Republic," but their symbols I've seen are completely different.