John, I have a similar tool but a little different shape.  It appears
yours has lost the handle.  An old time tuner made the one I have.

His daughter a long time ago said he would wet the hammer on the shank.
He would then heat the tool up and would steam the string impressions
out of the hammer instead of filing it out.  To me it was a logical
explanation of the purpose.  That was, at least, her tale.  I never
tried it because it would harden the felt.  Hope this helps.

My best,
Dell Urry