The author does not spell out Mr. White's third and last wish, but the reader can easily imagine what the old man wished for. He wished for the knocking to stop and for the knocker to go away forever.
A perfect fusillade of knocks reverberated through the house, and he heard the scraping of a chair as his wife put it down in the passage against the door. He heard the creaking of the bolt as it came slowly back, and at the same moment he found the monkey's paw, and frantically breathed his third and last wish.
Mr. White is under extreme pressure. His wife is trying desperately to open the door in the firm belief that it is her son Herbert outside. Mr. White believes it too. He is having trouble finding the monkey's paw with which he intends to make his third wish before his wife gets the door open. He probably would be unable to formulate his wish in precise words. No doubt he would have said something like, "I wish he would go away forever!" Those words would probably be sufficient to do the trick--assuming it really was Herbert returned from the grave and knocking for admission. The reader, of course, will never know whether it was Herbert or some stranger lost in a dark, unfamiliar area and trying to get some kind of help. Whether it was Herbert or a stranger, the wish has the desired effect.
The knocking ceased suddenly, although the echoes of it were still in the house. He heard the chair drawn back, and the door opened. A cold wind rushed up the staircase, and a long loud wail of disappointment and misery from his wife gave him courage to run down to her side, and then to the gate beyond. The street lamp flickering opposite shone on a quiet and deserted road.
The author has built up such a feeling of horror that the average reader probably believes it actually was the Whites' dead and mutilated son standing on the other side of the door and doing all that terrifying knocking. In fact, the reader can almost visualize what Herbert looks like! If the knocker had only been some ordinary human being, why and how did he disappear so quickly? The Whites should have been able to see him on the road. There is something about a loud knocking at our door that frightens most of us. We can imagine all sorts of things.