Rinse the granite sink thoroughly with hot water.
White rings around faucet on granite.
Hard water stains around the faucet.
And your hard water may be contributing as well.
It was deemed not a good idea as a plummer s putty ingredient tends to bleed through granite and leave the type rings you describe.
It had to do with using plummer s putty to seal faucets at stone level.
A water filter may not be sufficient to deal with hard water.
Maybe they used plummer s putty at your faucet connections.
For really stubborn stains try using a poultice or extractor.
These are formed by the water that flows into the home and is fairly common in most cities.
When hard water sits on a granite surface and dries it leaves a visible mineral deposit that often creates white rings especially around faucets.
There was a thread here a few weeks months ago about a similar sounding situation.
For this kind of stain use a specially formulated granite cleaning product like granite gold daily cleaner and scrub with a soft bristled brush then rinse and dry with a soft cloth.
For those tenacious water rings around a faucet resulting from hard water that sits on the surface try scrubbing softly with a brillo pad or gently scraping with a razor blade then wiping away the residue with a soft damp cloth.
I get that they do not sit directly on the granite but soapy water certainly does get onto the granite particularly around the soap bottle and sponge.
Hard water can create a calcium buildup which is also called limescale or lime deposits.
You need a water softening system.
You can also use a single edge razor blade to gently scrape away the residue or a safe on stone pad to scrub the area softly before rinsing and drying.
Scrub the granite sink with the scrubbing pad.