You can't use CCTransitionScene to change just the background. What you are looking for is CCActions.
But first, here is a sample of a simple "animation".
First init a SpriteFrameCache (that will store all your sprites):
[[CCSpriteFrameCache sharedSpriteFrameCache] addSpriteFramesWithFile:@"destructible-clock.plist"];
CCSprite *clock = [CCSprite spriteWithSpriteFrameName:@"destructible-clock3.png"];
clock.position = _countdownTimer.position;
Then when you need to change the sprite use setDisplayFrame:
//Update desctructible clock
CCSpriteFrame *frame = [[CCSpriteFrameCache sharedSpriteFrameCache] spriteFrameByName:[NSString stringWithFormat:@"destructible-clock%d.png",(int)(self.countdownTimer.percentage/25)]];
It's important that you understand SpriteSheets and/or SpriteFrameCache. Try this if you can't figure out how to make this work: http://www.raywenderlich.com/1271/how-to-use-animations-and-sprite-sheets-in-cocos2d
After that you can trigger the background swap with CCActions.