After their first evening together—a pretty chaste affair with a chaperone and her being married and everything—Denys gives Karen the gift of a pen in exchange for the awesome story she told the night before. He explains that it's kinda sorta local custom.
DENYS: We pay our local storytellers here.
It's not the same thing as giving her the ability to write. She can clearly do that on her own, and this movie is about nothing if it isn't about a girl doin' it for herself.
No, it shows her that he sees her talent and respects her as an equal. He's not talking down to her or dismissing what she can do or any other bits of mansplaining awfulness. That means a lot in a world like this, where women aren't exactly treated with the respect and dignity they deserve. He's better than that, and the pen shows us exactly how much.
He does the same thing with the compass he gives her later in the film. This time it's something from his world, not hers, but the message is the same. He knows she can put it to good use, and giving it to her is a sign that he treats her like an equal. (Now, if only he'd commit.) That makes both objects a sign not only of what Karen can do, but of Denys's belief in her.