These verbs mean to get back something lost or taken away. Recover is the least specific: The police recovered the stolen car.“In a few days Mr. Barnstaple had recovered strength of body and mind” (H.G. Wells). Regain suggests success in recovering something that has been taken from one: “hopeful to regain/Thy Love” (John Milton). To recoup is to get back the equivalent of something lost: earned enough profit to recoup her expenses.Retrieve pertains to the effortful recovery of something (retrieved the ball) or to the making good of something gone awry: “By a brilliant coup he has retrieved . . . a rather serious loss” (Samuel Butler).
After days of inquiries, he finally recovered his lost wallet.
1918, W. B. Maxwell, chapter 22, The Mirror and the Lamp:
Not unnaturally, “Auntie" took this communication in bad part. Thus outraged, she showed herself to be a bold as well as a furious virago. Next day she found her way to their lodgings and tried to recover her ward by the hair of the head.