I found this story on the Mrs. Daffodil Digresses blog here. "Telephone Face" is exemplified in the illustration of the man below.
“'What’s the matter with that man?' said the Observer, repeating his friend’s interrogation, as they passed a pedestrian wearing a most prodigious frown. 'Don’t you know what’s the matter with him? He’s got the telephone face.
“'Never heard of it, eh? Well, that shows that your powers of perception are not particularly acute. The telephone face is no longer a physiognomical freak, but a prevalent expression among the several thousand unfortunate clerks and business men who find extensive use for the telephone necessary. It is a distinctive cast of features, too, which can readily be distinguished from any other by one who can read faces at all.
“'The dyspeptic has a ‘face.’ His expression is fitful and disgruntled, but underlying it is a gleam of hope; the insolvent man, harassed by creditors, has another well-defined type of facial mold. It is haunted and worried, with a tinge of defiance in it; the owner of the ‘bicycle face’ has his features set in lines of deadly resolution; the ‘golf face’ displays fanatical enthusiasm and a puzzled look resulting from a struggle with the vocabulary of the game; the ‘poker face’ shows immobility and superstition; the ‘telegraph face,’ according to a well-known New York professor, is ‘vacant, stoic and unconcerned,’ but the ‘telephone face’ stands out among all of these in a class peculiar to itself. There are traces of a battle and defeat marked on it; the stamp of hope deferred and resignation, yet without that placidity which usually betokens the acceptance of an inevitable destiny. The brows are drawn together above the nose, and at times a murderous glint shows in the half-closed eyes of the possessor.
“'The peculiar feature about the man with the ‘telephone face’ is, that he always believes the day will come when he will be able to get the right number and the right man without being told that the ‘line’s busy,’ ‘party does not reply,’ or ‘phone is out of order.’ He is like the man who always backs the wrong horse, the poet with an ‘Ode to Spring,’ or the honest man seeking a political job, continually defeated, but ever dreaming of ultimate success.
“'I know of only one instance in which the dream was realized. A new girl had been installed in a telephone office without proper instructions— a most unprecedented case. A bookkeeper, grown gray in the service of a large mercantile house, picked up his receiver wearily. It rang the new girl’s bell, and like a flash, she said, ‘Hello.’ The bookkeeper gasped. ‘Is that you, Central?’ he asked huskily. ‘Yes,’ replied the unsophisticated maiden, pleasantly. ‘What number, please?’ The old man sat bolt upright and clutched the desk. ‘Give me purple six double-nine,’ he said, in quavering tones, and his weak form trembled as he spoke. Nimbly worked the fingers of the uninitiated telephone girl, as she struck a peg in the switchboard and quickly rang a bell. A voice at the other end responded promptly, and the bookkeeper wiped cold beads of perspiration from his brow before he answered. ‘Is this Jones & Company?’ he almost shrieked. ‘Yes,’ came the reply, full and clear, ‘this is Jones talking.’
“'A dull thud followed, and, when the other clerks rushed in, they found the old man lying still and cold, his right hand still grasping the receiver of the telephone, which had fallen to the floor beside him, and a smile of the most transcendent happiness they had ever seen upon his faded lips.'"
The original source was Said the Observer, Louis John Stellman, 1903. This is obviously satirical, but I wouldn't be surprised if many people read this and thought Telephone Face could be a real condition. This is especially true when you consider the previous Victorian focus on physiognomy (or the reading of facial and body structure in order to determine behavior, personailty, and morality). There was also a lot of popular confusion about Darwinism and evolution (namely, believing new inventions will affect our physical bodies–and people still believe this today, since some think our excessive use of texting and typing will mean we'll evolve with flattened fingertips, which is NOT how evolution works).