So, Jaime escaped without his iconic sword...It's probably too much to hope that Brienne is even in episode 6, let along that she has a speaking part. But what if there was a purpose to that little snippet of screentime?

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(I apologize in advance if this doesn't actually resemble a script format...)

...

Brienne stands alone, armored, staring over the remains of Kings Landing. She surveys the damage, until her gaze finally rests on the collapsed keep.

(offscreen) TYRION: He did love you, you know.

The camera pulls back to show Tyrion walking to stand behind her.

BRIENNE: I know.

Her tone is calm, decisive, with a hint of wistfulness but no regret.

TYRION: And he was happy. When he was with you, I mean. I'd never-

BRIENNE: -I know.

TYRION: But his past-

BRIENNE: (interrupting) Tyrion, I know.

She's not angry, really, but nor is she willing to discuss this any further. A moment of uncomfortable silence passes between them, and then Brienne looks around, and then down. She notices Tyrion is holding Widow's Wail. They both stare at it, remembering.

BRIENNE: He renamed it, you know.

TYRION: Really?

BRIENNE: Honor. After the battle of Winterfell, he named it Honor.

TYRION: He never was very imaginative.

They both smile. Then Tyrion lifts the heavy sword up and offers it Brienne.

TYRION: He - Jaime - he asked, if I survived, if I could, that I give this to you.

BRIENNE: He already gave me a sword.

TYRION: Yes, but this is it's partner. Forged from Ice, brought back together at Winterfell, to defend the living from the dead.

Tyrion holds the sword out toward her.

TYRION: They belong together. In the North, with you.

Brienne looks uncertain for a moment, but then she nods, and takes the blade. She turns back to look over King's Landing, and then north, toward her new home.

She'll be fine.