WoW...try soap and water...
I use GlassPlus and a soft towel, let it soak for a few minutes and it usually wipes right out with a little elbow grease.
Try a damp rag with some dish soap placed directly on the rag and work it in...
Are you sure it is plumbers putty and not caulk...normaly plumbers putty comes right off...
Stainless Steel Magic┐
Oops! solvent and cleaner will dissolve most anything sticky, including chewing gun, adhesives, etc.
SS can be somewhat porous, and most plumber's putty has some oil in it. Oil stains need a solvent to remove if embedded.
Important note - I'm not a pro
Retired Defense Industry Engineer; Schluter 2.5-day Workshop Completed 2013, 2014
If his are on the sink then anyone else who touches it will also leave marks. Bartender's Friend cleaner is usually what is used.