Fine lines / scratches on bathroom basin

[OldJoseph]

Our, relatively new, basin has a few fine lines on it, they look like hair. I've no idea how they got there, we only use it for hand washing and teeth cleaning. No nasty chemicals or boiling water.
Any ideas on how to get rid of them or thoughts on how they arrived in the first place?

Where on the basin are they? The very fine marks on the left hand rim of ours turn out to be watch strikes (titanium) and can be polished out with Plumber's rubber.

They are in the basin, where the water runs, they just look like my (very fine) hair. Plumber's rubber looks good, could it harm the basin if it didn't work do you think?

I doubt it could harm as it isn't abrasive. It certainly hasn't marked my porcelain basin in any way.