Have YOU ever gone through the tiring, agonizing effort to finally get a baby to sleep? After all that, you wouldn't want something to wake it up and make it start screaming, then you have to do that effort all over again.

I asked Ghost Boy about this recently when he appeared at my window. He said it had to do with them (Selleck and Guttenberg) possessing 5 kilos of cocaine.They were high as hell and tweaking at the time.

It is because they are afraid that the sirens will anger Ghost Boy.

Okay, these men were bachelors, who had no idea how to take care of a baby. She was crying all day, and they were exhausted taking care of her. When the siren woke them up, they shut the windows, and Peter stood over Mary with the cushion, I am assuming to block the noise. Even though, yes, it is Manhattan and sirens and the like are a regular occurrence, these men didn't want to take a chance at waking up a baby that took so long to fall asleep.
Also remember this: Mary was from a posh area of London, so she probably didn't hear those noises there.
They were clueless, and they were not taking any chances. Yes, Peter looked like an idiot, but he did not know what he was doing.

Like the others said, they were concerned about the noise waking up the baby.

you don't think they were freaked out by the ghost?

No, I don't have kids. But if I lived in a penthouse apartment who knows how high up in complete safety I wouldn't rush up and grab a pillow and brace it like an idiot, as if an intruder was about to come in, just because of a siren in.wait for it.Manhattan.
"Hey, let me ask you a question, bonehead: Why are you trying to ki-ki-ki-killllll me?!?!?"

Obvously you don't have kids. When kids sleep they can easily be startled and awaken by loud sounds especially a car alarm or thunder. When the car alarm went off they jumped up 1. It may have Startled themselves and 2. To quickly rush over and close the window in case it woke her up. That's all

I think they were more worried about the sirens triggering Mary to cry.

You sure? Tom Selleck clearly gets up and into a defensive, protective position, as if to be ready for an intruder. Steve G. Rushes to close the windows as if to keep someone from getting in. At least that's how I've always seen it

Because they are afraid the sirens are going to wake up the baby.