The Dumb (?) Waiter is the title of an obscure, short-lived and most likely lost comic sketch written by P. G. Wodehouse and Lennox Pawle, first produced in London at the Tivoli Theatre on October 24, 1910, according to A. Nicoll, English Drama, 1900-1930. The Beginnings of the Modern Period (2009), vol. 2, p. 1035. It is not mentioned in D. Jasen's The Theatre of P. G. Wodehouse (1979).
The most complete review I have been able to find is in The Era for October 29 of that year. It provides a few details of the piece's plot, language and humor:
THE TIVOLI.
Mr. Joseph Wilson's latest novelty at the Tivoli is a sketch without a plot, from the joint pens of Mr. Lennox Pawle, the popular comedian, and Mr. P. J. [sic] Wodehouse. It is entitled The Dumb (?) Waiter, the ironical significance of the adjective of the title being marked by a note of interrogation. In a restaurant scene a deaf-and-dumb gentleman and a Hebrew of uncultivated manners are dining. The Jew, after addressing several observations to the deaf mute, appropriates his evening newspaper, which is promptly snatched back by the silent one. After one or two little skirmishes the waiter arrives on the scene. He is quite a greasy specimen of his class, but his clatter of speech is prodigious. Like Gratiano, he speaks an infinite deal of nothing. His deaf-and-dumb customer has, he thinks, a sympathetic soul, and when he pours his family history into his ear, with incidental references to the doings and love-troubles of a kindly-hearted innkeeper, he has no idea that his talk flows "in one ear and out of the other." The old gentleman at last understands that he is being spoken to, and taking a small scrap of paper, he scribbles thereon: "Any statement of importance you have to make you must put it in writing. I am deaf and dumb." The sketch has the merit of giving a droll comedian a real chance as a humorist, and its chief recommendation is that it introduces to the London variety stage Mr. John Humphries, of whom too little is seen in the West End. Such a capital comedian should be permanently established in the metropolis. The music halls, at any rate, can do with him, for his waiter is a joyous optimist, and a refreshing exponent of a Cockney type as amusing as it is lifelike. Mr. Humphries may be said to have "found himself" in the halls. He should remain there.