Actually there is a little trick
when you create a backrground or paste the meez,or....anyhow
...., when you select a zone, you got some kind of a regulator...this regulator serves at indicating how important the selection is and thus how close to the lines you'll be:
sorry my gimp is french :S so yeah just make it so that it select the closer to the outlines (not too much otherwise it might color the inner part of your selection...
It can HELP at REDUCING white outlines but for sure doesn't solve the problem 100% of the time...some users know how to do it even more precisely but that's the only way i know sorry...hope it helped...