Anytune utilizes two time-stretching algorithms – Pro and HQ. HQ is available with Anytune Pro+ or when you add the Studio Pack to the Free version.
The Pro algorithm usually handles spoke voice very well and in some recordings better that the more resource intensive HQ algorithm.
You can demo HQ to see if it is better by going to Settings > Audio Quality and enabling HQ. But it will only let you try the first 20 seconds of a song.
Also make sure you do not have any other affects added to the song. Tap the Song Title and Tap Reset Music Settings.
You could also send us the audio file and we will give it a try to see if there is any optimizing that can be done.