My grandma did that too, and I actually kept a little jar of the best pieces. It makes you actually LOOK at what you're walking on. Grab a clear container and start picking out the milky white, the pink, even the ones with little lines in them.
About picking out the milky white pieces, I see it differently. Looking so hard at the ground makes me miss the trees and sky above. I'd rather just enjoy the walk without hunting for things to keep.