When Black Mumba comes to see Hattori Hanzo, she is wearing a white T-shirt and holding a bag. She sets the bag down and has nothing else. Yet when she follows him up to the sword room, she is now wearing the coat.
I doubt she stopped him so she could put the coat on.
This observation does not, alas, qualify. The jacket might have been tucked away inside her bag and the audience is not informed of how much time lapsed between the two scenes. For all we know she ate her sushi and finally got some sake before Hattori invited her upstairs.
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