I don't remember ever being able to quit the local levequests on the OB, but I never accepted any levequests I didn't want in the first place. The only solution I can think of is to fail them on purpose, or just do what you can with them. You still get Physical Level EXP if you complete them, so not a complete waste. Of course that costs whatever it does to buy the items to use those particular jobs.
It's kind of crappy you can't just quit a leve (or at least the option is clear) even if it counted against your total until reset. I did a few of them that were for camps that I had no idea how to find. So they sat there, completed and in my journal, taking up space.
Wow if this is the only way to "quit" a local levequest, it's horribly horribly broken. So I have to run all over town looking for the NPC that sells the tool that lets me be an alchemist or chef or whatever, I have to then spend 10 minutes of my time actually doing the levequest, and that's the only way I can get it out of my levequest list? The whole reason I want to quit the quest or exchange the quest is because I don't want to do it!