This article applies to:
7.x Briefcase for iOS
The New flag is a SharePoint feature that displays and functions in the same way in Briefcase for iOS
When a document or item is added to a list or library, it is labeled as New for 24 hours. This is marked from the time the document is added to SharePoint, so modifications to the document or new versions do not affect the flag.
Currently there is no setting to remove this UI element.