Nona wants you to recover some of the gold that has been paid to Dunlendings by Saruman's agents.
'I have spent some time watching the people of Barnavon, ${PLAYER}. Saruman has paid no small sum of gold to the leaders of Barnavon for their loyalty, and I fear what that might buy him.
'The iron mines of Carreglyn are at stake. The men of the upper village will attack you on sight. Defeat them and take the gold with which they have been bribed. Teach them the true cost of forgetting their honour as Men of Dunland.'
Hostile Dunlendings in Barnavon carry the gold with which they were bribed.
Nona wants you to defeat hostile Dunlendings throughout Carreglyn, but especially in the upper village of Barnavon, and take the bribing gold from them.
Nona is in the village of Barnavon, in Carreglyn.
You have retrieved the bribing gold and should bring it to Nona.