"It smooths the way in"

The softener is the sorry that opens a request. "Sorry, quick one." "Sorry to bother you." "Sorry, can I just." You'd say it helps. It signals that you know you're interrupting, and the signal makes the interruption easier to take.

Consider what the softener tells the listener about the request. It says this is an intrusion. It says the asker knows it's an intrusion. It says the asker feels they need permission to make it. All of that is information, and all of it is false, because the question was your job and answering it is theirs, and nobody is intruding on anyone. The softener has taken an ordinary exchange between colleagues and framed it as a favour being begged, and the listener, who had no such thought until you supplied it, now has it.

An earlier book in this series, about not asking for help, describes the over-apology around a request and what it does to the request's chances. I'll borrow one point. A request that arrives apologising for itself invites the listener to treat it as optional. "Sorry to bother you, could you possibly" is a sentence with three exits built in, and a busy person takes an exit. "Quick one, when's the deadline for the north report?" is a question with no exits, and it gets an answer. Dev gets answers.

There's a second thing the softener does, and it's slower. Every "sorry, can I just" in a meeting is a small announcement that you don't think you have the floor by right. Said once, nobody notices. Said at the start of everything you say for three years, it's the read, and the read is that you're the one who asks permission to speak, and people who ask permission are given it, or not, by people who don't.

Smoothing the way in isn't what the softener does. It roughens it, by turning a question into an apology with a question attached, and the method in chapter 21 is a set of sentences that get the question into the room without the apology in front of it.