When we talk about "Scotch-brite" are we talking of wire- or plastic- wool?
Genuine basalt (the dark-grey, sparkly surface-plate stuff) and indeed granite (lighter-coloured, highly-mottled, kerb-stone stuff) are extremely hard. Basalt is even melted and cast into liners for industrial plant handling very abrasive slurries and powders (MP about that of cast-iron, but more viscous.)
So although I advise against making it a habit, I can't imagine a single, gentle cleaning with a plastic scouring-pad or even a wet, soapy 'Brillo' pad will really damage either rock beyond interferometry-test depth.
For normal cleaning use white spirit, meths or kitchen work-top cleanser, on cloth.
(Both rocks are made of silica, second in hardness to diamond; and metal-silicates, a bit softer but generally still harder than steel.)
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Just don't use scourers on your shove-ha'penny slate though….