The act of bringing something back is called retrieval. When you throw a tennis ball to Fido and he brings it back to you, that's retrieval.
When you lose something and get it back, that's retrieval, whether it's a tote bag you accidentally left at the library or a file you can't find on your computer. In fact, the word retrieval is a common one in computer science, meaning "the act of accessing information." The word comes from the verb retrieve, which was first used in the fifteenth century to describe a hunting dog bringing a dead bird back from a field.