I think it is just a small production error. The prop note is already attached to the bird and Dom is just told to "act" like he is attaching it.
If it is part of the story then A: He doesn't actually attach any note, and Claire would have to be pretty dumb to not notice this. B: He switches notes and Charlie is a lot more cunning than usual.

I like everyones thoughts on the final outcome of the bird.
How about this one:
Locke and dear old dad make up and they go bird hunting. Dad bags the bird and Locke finds the note. Locke reads it to find that Charlie did switch the note with a joke about Locke. So Locke gives the little limy runt another beating. Desmond saves him again, and Claire leaves Charlie for Des cause she wants a man who can take care of himself.

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Doctor playing golf. Woo, boy howdy, now I've heard everything. What's next, cop eating a donut?