A sales man told me not to use any chemicals on a granite surface. He said just use soap and water.

I don't have granite but I do have the same residue and I clean it with a bit of vinegar, let it set a bit and brush it away.

I wouldn't use vinegar on granite, it is a mild acid. I remove mineral build up with a single edge razor blade.

You could be right about the vinegar. The poster may her faucets set directly onto the granite, that would be a very different situation. Mine are set on the sink and I keep a small spray bottle of vinegar to soften the hard water deposits, then scrub it with a toothbrush. I use it for that and in vases to get rid of the water lines there.