The story revolves around Ginjiro Mugan, a former gangster and Minami Takeshi a private investigator and their Debt Collecting business "GetBackers".
The misspelling likely stems from phonetic confusion for non-native Japanese speakers. In Japanese, modotte (from modoru , to return) is the correct conjugation. "Midotte" does not have a standard meaning in this context, but because of how widely the original series is searched, the typo has become a common "entry point" for users trying to find the series online. Cultural Impact
You're referring to the popular Japanese manga and anime series "Gaki ni Modotte" or "Gangsta" but I think there might be some confusion. There's another anime with a similar title which is often romanized as "Gaki no Tsukai" but I believe you are asking for information about "Gaki ni Modotte" also known as "Get Backers".
This genre taps into the universal fantasy of "regressing" or time-traveling back to one's childhood with the knowledge and maturity of an adult to "fix" past mistakes or live a more fulfilling life. The Core Concept: "Starting Over" as a Child