Katharine Clifton's favorite Monopoly piece would be the thimble. (What would Almásy choose? The dog? The (loose) cannon?)
During their first sexual encounter, Almásy tears off Katharine's white dress. Later, he is seen sewing it back together. It's a little gender reversal—the man sewing for the woman. Katharine doesn't know how to sew, and she says,
"A woman should never learn to sew, and if she can she shouldn't admit to it."
This, like everything in this movie, goes to the theme of ownership. A woman would be more subservient to a man if she sewed his clothes.
Almásy's first gift to Katharine is given with irony: it's a thimble. But it's not for sewing. It's full of saffron, a spice. Katharine wears the thimble of saffron around her neck, and she's wearing it when she crashes in the desert. Seeing it startles Almásy… because she broke up with him. But she tells him,
"Of course, you idiot, I always wear it. I've always worn it. I've always loved you."
This prompts Almásy to cry, one of the few scenes he shows emotion.
One of the movie's more striking images is after Almásy returns to retrieve Katharine's body. He paints her face with the saffron from her thimble. It's an act that's half eulogy, and half a final expression of ownership.