Quick question: Gouge in Floor

Hi guys, I have a real quick question, hoping that someone can help.

I have a solid (tongue and groove) timber floor which was sanded and re-finished with Cabots CFP Water Based a couple of months ago.

On the weekend I dropped a venetian blind and the corner of the aluminium frame dug into the floor and lifted a piece of the wood (about 2.5 cm long, 0.5cm wide) which is still attached to the floor at one end.:doh:

My question is what is the best way to repair this gouge?
I figured I have two options:
1. Glue the piece back down with wood glue/liquid nails and fill any remaining spots with putty.
2. Remove the hanging piece of wood and just fill the entire gouge with putty.

It is a minor issue, but does anybody have advice as the best solution that would provide a lasting repair? (I assume that just gluing the hanging piece may not be a structurally sound solution).

Thanks a heap,
Dan


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