Hone counters are a new kind of counter in The Hobbit, and they power up Equipment. For each hone counter on an Equipment, the creature it is attached to gets +1/+0.
It's a rule, not an ability
The pump from hone counters is not something the creature has as an ability. It comes straight from rule 122.1j, so anything that cares about abilities will not see it.
Reconfigure creatures only pump when attached
A Reconfigure creature with hone counters on it does not pump itself while it is a creature. It only gets the bonus once you reconfigure it onto another creature.
Auras get nothing
Hone counters only do anything on Equipment. If you somehow move them onto an Aura, they just sit there doing nothing.