The reason why Mrs. Sappleton keeps her window open is because her husband and her brothers go hunting quite a lot (shooting). That particular day, the shooting party had been out in the marshes and Mrs. Sappleton knew that they usually would come that route back to the house. Since she did not want them to stain the carpets, she would let the window open so that they could come through the window, rather than through the front door.
..."my husband and brothers will be home directly from shooting, and they always come in this way. They've been out for snipe in the marshes to-day, so they'll make a fine mess over my poor carpets. So like you men-folk, isn't it?
It is a practice which Mrs. Sappleton's niece, Vera, used to make up a story that would scare house-guest Mr. Frampton Nuttell away. It is precisely what it did for, when the men returned, they even asked who was it who bolted out of the house in a frenzy.
Here we are, my dear," said the bearer of the white mackintosh, coming in through the window; "fairly muddy, but most of it's dry. Who was that who bolted out as we came up?