Black streeks from molding

I am getting black streeks that are a pain to get off. It is coming from up under the rear modling that wraps around the rear of the convertible top, from the side mirrors and some from the window moldings... I know it is just dirt and grime that is up under it and the side moldings and side mirrors should not be a problem to take off and clean. The problem is the wrap around molding on the back... I have heard it is a royal pain to take off. So is there any other way to stop it from streeking?
 
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