They went down into the basement; the cats, who seemed to have fallen into the sleep of exhaustion, awoke at the sound of the approaching footsteps and mewed piteously.

Jane was at the foot of the stairs before she saw it was not her brothers whose coming had roused her and the cats, but a burglar.
She knew he was a burglar at once, because he wore a fur cap and a red and black charity-check comforter, and he had no business where he was.
If you had been stood in jane's shoes you would no doubt have run away in them, appealing to the police and neighbours with horrid screams.

But Jane knew better.

She had read a great many nice stories about burglars, as well as some affecting pieces of poetry, and she knew that no burglar will ever hurt a little girl if he meets her when burgling.

Indeed, in all the cases Jane had read of, his burglarishness was almost at once forgotten in the interest he felt in the little girl's artless prattle.
So if Jane hesitated for a moment before addressing the burglar, it was only because she could not at once think of any remark sufficiently prattling and artless to make a beginning with.