What is the 'consistancy' of the grim? If it's nothing of a 'physical consistance' and is more like just 'dirty' and worn out, you can consider refinishing it. This would involve sanding, staining, and applying poly.
My best to ya and hope this helps.
Jay J -Moderator
PS: What are you thinking you can do to 'clean up' the banister? (I can't see it from here ...)