Couldn’t you find some way to remove this stain?
This is the noun version of 染. A dye would seem like the right answer, but what else is a dye? If you get it on you when you don't want to get it on you, it becomes a stain.
The reading is unlike what you learned with this kanji before. Just think about how you have this stain on your shirt, all because you were trying to dye some sheep (し) and they didn't like it. So now you have a big dye and sheep poo stain. How were you supposed to know sheep don't like being dyed?!