"A Haunted House" by A. A. Milne
This story shortly follows "The Watson-Touch". It is a ghost story with some funny/interesting elements that could or already have been used as a template for the Special and Mary's character in particular.
The narrator tells us, that he has moved in a haunted house.
This house had only one owner before, her name: Lady Elizabeth Watson-Watson (no, I'm not kidding you! And we have been speculating before about the meaning of Mary's middle name) and her "nom-de-guerre" is Lady Elizabeth Mullins.
Its first and only tenant was a Mrs. Watson-Watson, who lived here with her daughter. Add her three servants, and you have filled the house. No doubt she could have stowed people away in the cellar, but I have never heard that she did; she preferred to keep it for such coal and wood as came her way.
And as soon as the family moves into the new house, there are still lots of letters arriving for Lady Elizabeth.
also letters for Mr. J. Garcia arrive; eventually a letter arrives even on a Sunday - but it is for Sir John Poling. The narrator knows none of these people
The narrator has two explanations. One has a very pragmatic reasoning:
“[...] our address has become in some way a sort of typical address [...]. When a busy woman puts our address on an envelope beneath the name of Lady Elizabeth Mullins, all she means is that Lady Elizabeth lives somewhere, and that the secretary had better look up the proper address and write it in before posting the letter. Every now and then the secretary forgets to do this, and the letter comes here.”
But the more intersting explanation is this one:
“I think that our house is haunted by ghosts, but by the ghosts of living persons only, and that these ghosts are visible to outsiders, but invisible to the inmates.”
Another possibility for the ghosts in the Special? (and Mary is one of them?)