Utlac told you more about the Orc-raid that greeted the Rohirrim upon their arrival in the East Wall, and he wants you to help him recover an arrow he spent in haste as the Orcs fled.
'I have a confession to make to you, ${PLAYER}. I know that I seem level-headed, as fine an example of a steadfast Man of Rohan as you could hope to meet, but I have a secret. I have been known to lose my temper on occasion. Nay, look not with disbelief!
'It seemed that we would not be able to hold out against the Orcs that ambushed us upon arriving at the East Wall, but we prevailed. As the Orcs broke and fled for the safety of the trees, I loosed my prized red-fletched arrow at an Orc's retreating back. I did not need to loose, but I was angered! I let that arrow fly and saw it pierce him in the leg.
'But he did not fall! He kept running, and he took my prized arrow with him! He ran to the south, ${PLAYER}. Perhaps he followed the streams that flow out of and back into the East Wall, using them for guidance. Go that way and find his body, for surely he has succumbed to his injuries by now, and retrieve my prized arrow!'
The Orc on which Utlac wasted his prized arrow ran south of Mansig's camp, and the archer thinks that he may have followed the course of the streams as they flow out of and back into the East Wall.
Utlac feels badly about wasting his prized red-fletched arrow and wants you to find the Orc that carried it away after the ambush.
Utlac is at the Rohirrim-camp in the East Wall.
You have recovered the red-fletched arrow that Utlac wanted you to find and should bring it back to him.