I should have also mentioned that the reason why someone would have mixed plumber's putty with linseed oil is because window glazing putty is clay mixed with linseed oil.

Linseed oil is a "drying oil", which means that it reacts with the oxygen in the air to form a solid. This is why window glazing putty hardens up after a while.

Plumber's putty is the same as window glazing putty, but it uses a "semi-drying oil" which reacts with the oxygen in the air to form a weak solid. So, plumber's putty will eventually harden up and become brittle just like glazing putty, but it doesn't stick well to surfaces (like wood and glass) like glazing putty does.

I think that someone has mixed linseed oil into plumber's putty to make something that's gonna behave more like a mixture of clay and oil based paint than plumber's putty. And, why they used it on the underside of the sink don't make no sense neither.

And, I'd presume they used that same stuff between the strainer basket flange and the sink bottom, so it might be a fight to get that strainer basket out too.