If you were to get the repellent stick in any way besides completing the optional task it was used for, you can't get rid of it. why?

It's tagged as a quest item.

But when people do the optional part of the quest they are to store it in a locker
people that bought it back or stole it cant.

Once you complete the mandatory part of the quest, the quest item tag is removed from the stick, and then you can drop it, store it or sell it. The tag may come back if you repurchase or steal the stick after dropping it once. I've never tried that - once I finish the quest (optional and mandatory parts) the stick goes into my weapons locker and stays there. It's pretty useless once you're done with it.

A lot of quest items in this game are glitched like that - once you pick them up you can never get rid of them.