Be warned that this will also remove the very thin gold wash! I'm not sure if you can remove the rust and keep the gold wash underneath.
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Like you I have never had an issue - apart from this one razor. Unlike the Filarmonicas and Pumas, the band on the BL is not tight, therefore it's quite easy for moisture to creep underneath and then you can't get at it to perform the usual cleaning routine.
Like I said, the best thing is to take it off so that you can ensure the tang is properly dry. In terms of handling, there is no noticeable difference either with or without the rubber.
Indeed, the rubber on the tang in the BL is utterly useless