I figured out what I needed to do. It wasn't anything special really. It just required a better understanding of what was all possible.
Basically all I had to do was add a basic opacity animation to the layer with text in it.
// My original code for creating the text layer
CATextLayer *titleLayer = [CATextLayer layer];
.
.
.
[titleLayer displayIfNeeded];
// the code for the opacity animation which then removes the text
CABasicAnimation *animation = [CABasicAnimation animationWithKeyPath:@"opacity"];
[animation setDuration:0];
[animation setFromValue:[NSNumber numberWithFloat:1.0]];
[animation setToValue:[NSNumber numberWithFloat:0.0]];
[animation setBeginTime:1];
[animation setRemovedOnCompletion:NO];
[animation setFillMode:kCAFillModeForwards];
[titleLayer addAnimation:animation forKey:@"animateOpacity"];