The Alfred Hitchcock Hour (1962) : 1x3

Jim Mallory is a forest ranger who along with his wife Linda, have adopted a girl named Anne. The couple have never told Anne that her parents died in a bizarre murder-suicide for fear that the news might disturb her. A blackmailer contacts Jim and demands money. He says that he will tell Anne the secret of her past if Jim doesn't pay up. Jim agrees to pay, but informs the police. The blackmailers figure out that something is up and change the site of the money drop. Later the blackmailers get into an argument and one of them is killed. When the police find the body, they suspect Jim Mallory. Jim manages to catch the blackmailer to clear his name, but he doesn't get to him in time to stop her from telling Anne the secret about her parents. Anne is troubled by the news, but manages to take it in stride. She tells the Mallorys that she loves them and has always considered them her real parents.