Yes, Deselect the quest. Problem solved.
What if you only have one quest? One quest can't be deselected, you can only switch through different quests. At least it was like that in Oblivion and I think FO3 as well.
And compass icons can't be deselected.
Anyway... Fallout 3 had an .ini option to toggle quest markers. Don't think it's above the head to say that this option could be as a gameplay option now, seeing there have been lots of discussions here on the forums about it... and that I think pretty much everyone would like (or not dislike) a toggle option.
It makes a really big difference for those who care about it, and a lot of people do seem to care. And it's a little piece of cake to do that a dev can probably do on an afternoon.