The stain on the windowsill conveys the same idea.

So does the card on the body, which might have been prepared in the house.

That all fits into your hypothesis, Watson.

But now we come on the nasty, angular, uncompromising bits which won't slip into their places.

Why a cut-off shotgun of all weapons--and an American one at that?
How could they be so sure that the sound of it would not bring someone on to them?
It's a mere chance as it is that Mrs.Allen did not start out to inquire for the slamming door.