Admittedly, I don't fully understand your question. I have never heard of motivated forgetting
I have, however, heard about Freud and his defense mechanisms. Repression, perhaps? Repression is an unconscious action that keeps anxiety provoking memories out of consciousness to make someone feel better. Or better yet Suppression, which is a conscious act to keep negative thoughts out of your mind. Either of these could be described as motivated forgetting.