Not an Infinity Scarf
Mary's scarf is a scarf for all seasons. It's light. It's goes with everything. And it's symbolic of how some men treat women: like disposable playthings. That never goes out of style. (But it should.)
Early on in her affair with the king, naïve Mary thinks their love will last forever. But if she paid attention to how Henry treats her scarf, she'd realize how wrong she is.
What actually happens? Well, Mary gives it to King H right before a joust. "I'll wear it against my heart," (2.394) he says. It's so romantic we could just gag.
At this point, Henry treats the scarf—and Mary—like it's the most important thing ever to him. But it's only important in the moment. By the end of the joust, Henry has dropped it, and he doesn't even know it's gone. Similarly, do you think Henry misses Mary one iota when he last moves on to Anne? Nope, didn't think so.
Later, the Queen Katherine finds the scarf and returns it to Mary. "It looked like a sorry bit of cloth, something you might wash a floor with" (2.461). Mary is a commoner, and the queen reminds her of this. Mary needs to watch her step, or instead of helping the queen, she might be scrubbing the floors herself.
Or the queen might order someone to scrub the floors with Mary's face.
When Mary brings up her hurt feelings to Henry, she learns he has the same regard for her feelings that he does for her scarf. He blows her off, saying, "You are not my mistress, madam, nor my wife" (2.495). This is pretty ironic, because Henry doesn't treat his wife or mistresses any better than other women. But don't tell that to Henry if you want to keep your head.