Early on in the film, we watch Hildy and Walter walking through the newsroom. Well, they're not doing anything as dull as "walking"—Walter's striding and Hildy's sashaying.
Walter goes through a door and lets it slam back onto Hildy. Hildy then reprimands him—in fast-paced, snarky dialogue—for not being chivalrous. They come to a second gate, and Hildy illustrates the right way to hold it open, letting Walter walk through. They then come to a third gate… and Walter again goes through first and lets it slam on Hildy.
If Walter's trying to get Hildy back, it seems like he's doing a poor job of it. He's not treating her with consideration; he's being a deliberately rude jerk. Do people usually let doors slam on the woman they love?
But actually Walter is being canny. His whole pitch to Hildy, his effort to win her back, is based on his argument that her second most important identity is as a woman. Her first identity? Walter tells it like he sees it:
WALTER: You're a journalist!
Walter's appeal is to Hildy's professional ambition. He's in love with Hildy the journalist, not Hildy the would-be domestic goddess. By slamming doors on her, he's saying (in that smooth-as-butter Cary Grant voice),
WALTER: Hildy, I think too much of you to treat you with kid gloves. You're a reporter. You can keep up with me. I'm treating you as an equal—which means I'm treating you as sloppily as I treat everyone else!
And you can see from how Hildy reacts that she's not really offended. She's amused. The two are playing together—or, if you prefer, flirting. Walter's letting her know it's more fun to joke with him than it is to be put on a pedestal by Bruce.
Even if some of those jokes can swing back a bit hard against the knees.