The spelling of the phrase "forget its" may seem puzzling to some. However, by looking at its phonetic transcription, it becomes clearer. The word "forget" is pronounced as /fərˈɡɛt/, while "its" is pronounced as /ɪts/. The apostrophe in "forget it's" is used to indicate a contraction of "it is" or "it has", whereas "forget its" simply refers to the possessive form of "it". Thus, the correct spelling in this case is "forget its".
The phrase "forget its" is not a commonly used term or phrase, and as such, there is no specific etymology associated with it. It is possible that it could be a typo or a misinterpretation of another phrase or word.