Why does the Valyrian Steel Oathkeeper use Dunk's Coat of Arms?

Question

The Valyrian Steel Oathkeeper is pretty accurate and even uses red Damascus steel to make it look closer to the original from the novels.

However, for some reason it appears to use a depiction of Dunk's Coat of Arms, a green shooting star above an elm tree proper on sunset:

As far as I know Oathkeeper was made for Jaime Lannister:

Tyrion put down Joffrey's sword and took up the other. If not twins, the two were at least close cousins. This one was thicker and heavier, a half-inch wider and three inches longer, but they shared the same fine clean lines and the same distinctive color, the ripples of blood and night. Three fullers, deeply incised, ran down the second blade from hilt to point; the king's sword had only two. Joff's hilt was a good deal more ornate, the arms of its crossguard done as lions' paws with ruby claws unsheathed, but both swords had grips of finely tooled red leather and gold lions' heads for pommels.
"Magnificent." Even in hands as unskilled as Tyrion's, the blade felt alive. "I have never felt better balance."
"It is meant for my son."
_{A Storm of Swords, Tyrion IV}

Who then gifted it to Brienne of Tarth:

Brienne approached as if the bundle was like to bite her, reached out a huge freckled hand, and flipped back a fold of cloth. Rubies glimmered in the light. She picked the treasure up gingerly, curled her fingers around the leather grip, and slowly slid the sword free of its scabbard. Blood and black the ripples shone. A finger of reflected light ran red along the edge. "Is this Valyrian steel? I have never seen such colors."
"Nor I. There was a time that I would have given my right hand to wield a sword like that. Now it appears I have, so the blade is wasted on me. Take it." Before she could think to refuse, he went on. "A sword so fine must bear a name. It would please me if you would call this one Oathkeeper. One more thing. The blade comes with a price."
_{A Storm of Swords, Jaime IX}

So why does the plaque use Dunk's coat of arms?

Answer 1

Brienne had Dunk's arms painted on a shield while travelling through the Crownlands and Riverlands

After being accused of murdering Renly, Brienne was travelling North to try and find Lady Stark's daughters and protect them. After having been given Oathkeeper by Jamie, she can no longer bear the arms of house Tarth, as she would be marked a murderess. She therefore recalled the arms of a House she'd never known, which happened to be those of Ser Duncan

The arms of Tarth were quartered rose and azure, and bore a yellow sun and crescent moon. But so long as men believed her to be a murderess, Brienne dare not carry them.
_{A Feast for Crows: Brienne II}

"You did beautifully," she said, when the woman showed her the freshly painted shield. It was more a picture than a proper coat of arms, and the sight of it took her back through the long years, to the cool dark of her father's armory. She remembered how she'd run her fingertips across the cracked and fading paint, over the green leaves of the tree, and along the path of the falling star.
_ibid.

Answer 2

In A Feast For Crows, Brienne has a new shield painted, using a design that she once saw on an old shield in her father's armoury -- and that design is Duncan the Tall's, suggesting that he ended up in Tarth.

The arms of Tarth were quartered rose and azure, and bore a yellow sun and crescent moon. But so long as men believed her to be a murderess, Brienne dare not carry them. “Your door reminded me of an old shield I once saw in my father’s armory.” She described the arms as best she could recall them.

The woman nodded. “I can paint it straightaway, but the paint will need to dry. Take a room at the Seven Swords, if it please you. I’ll bring the shield to you by morning.

...

The captain’s sister found her in the common room, drinking a cup of milk and honey with three raw eggs mixed in. “You did beautifully,” she said, when the woman showed her the freshly painted shield. It was more a picture than a proper coat of arms, and the sight of it took her back through the long years, to the cool dark of her father’s armory. She remembered how she’d run her fingertips across the cracked and fading paint, over the green leaves of the tree, and along the path of the falling star.”

So the picture simply shows Brienne's sword and shield as they appear in A Feast For Crows.