Gum Booger

A Gum Booger is the kind of annoying thing you can't successfully get rid of without spending a lot of time and effort, and even then it's difficult to complete.

Taken from nose-picking, when you hook out a booger that's moist gummy & sticky. No matter how much you might flick it or try to rub it off your finger and on to something else, it refuses to go. The only way you can remove it is by wrapping the entire fingertip in a rag and wiping it off. But if you had a rag in the first place, you wouldn't have had to pick it out.

Applies to:
An annoying person who just won't quit or go away
An annoying ad on TV that keeps on popping up during CSI
A driver who refuses to overtake but tailgates you and insists on matching your speed however much you speed up or slow down.
The annoying relative who always calls on the phone when you're really getting into a session of early morning sex.

among others.