It should fade completely, if it's from the beer being "green".
What yeast strain did you use? I've noticed that some British yeast strains produce that flavor, and if it's a yeast characteristic it might not fade as much.
Edited because I'm a dork- WLP028 is the strain, as noted in the first post. Duh! Well, that strain is supposed to be "clean" so unless you fermented too warm, it is probably just from the beer being young and some aging should fix it.