I've found something that cleans the red Sharpie ink off the linoblock. It had to be something that would clean the ink, but not damage the lino. The oil that I usually use to clean the block didn't work. Alcohol didn't work. Eventually, we found something that worked: nail polish remover. The stain is still on the block, but it doesn't print anymore.
I reprinted the block in slightly warmer colours (but without the red!).