I think Ariel is doing the reverse demo thing when we saw Hook, he was in SB and broke into Rumble’s shop to get is hook and placed it on his right arm even though Rumble took Hook’s left hand and he was in FL with Cora.
Ariel starts in NL, and ends up in SB but this has to have something to do with Grumpy not Belle the only thing that Grumpy could have is that fairy dust in the mine unless there is something else that could be in the mines. What Ariel is giving to Belle is a note or instructions that she is passing to Belle it can’t be her contract because Gold/Rumple kept them remember Cinderella breaking into to Gold’s shop to get hers back.
I don’t know what is in her left hand though could be she got her voice back from Regina/Ursula in exchange to delivering a message.