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Removal is difficult at best. Linseed oil really does not dry as do most conventional coatings, and it absorbs into pores. I would start with paint thinner and scrub with #00-000 steel wool and rags. Let the thinner sit for 5-10 minutes and wipe first then scrub. I would then try paint stripper, following the instructions above, but with out the steel wool. There is also an absorbent powder, that sucks up oil, but I couldn't find it. You can also get into acids, but they are dangerous. Make a friend at the paint dept. of your local big home supply store, they may have other ideas. .There are a lot of solvents on the market, but most can kill you. Found it. It's called "Oil Stain Removal Powder" and sold by Home Depot and online.

Use turps or turps substitute and clean rags; that way you know you won't make it even worse. Eventually, hopefully, you will dilute the linseed oil down to the point that you can once again see the attractiveness of that grey slate but it will always be at least one shade darker.

It's too late now, but there is a slate dressing made for the purpose, but even that would have made it darker.

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i would guess that if they use dish soap to remove oil from the animals caught in an oil slick

then you could use it to remove the oil from that aswell