An interesting study based on the adage “forgive and forget.” Here are some key points:
- They base the study on forgive first in order to forget.
- Forgiving may be a coping strategy: to forget the upsetting memories of the bad transgression.
However, with the last one, I often wonder why some people hold grudges. Is it because holding on to the bad memory is a way to keep one’s distance from that person? Perhaps holding on to grudges is a way to still protect the self in a way. Yet the article presents forgiveness as a form of control. From the article itself:
From the perspective of cognitive science, overcoming strong negative emotions toward the person who did us wrong and quashing impulses for retribution or vengeance — processes that are critical to forgiveness — may be seen as a function of executive control.
And research suggests that this executive control is also involved in our ability to forget something when we’re motivated to forget it.
Still, could holding a grudge also be seen as a function of executive control. After all, if this person wronged me, I hold a grudge in order to have executive control of the situation. Or perhaps the grudge, and the transgression, is controlling me!
Shaun Miller's Ideas 
I believe holding a grudge gives a superficial sense of control via self protection, but the grudge ultimately becomes a self prison; often without the grudge holder realizing it.
Forgiveness is important for own peace of mind. It is like not giving undue importance to someone or some event that can do nothing positive except give pain. Forgiveness is like a self healing process. Forgetting happens automatically with passage of time as the memory fades. Faint memory is enough to keep the person alert from getting hurt again. If we forget completely we may get hurt again in the same way. Which is not describable. However that memory should never stay in the forefront or guiding force for vengeance.