At the bottom of the memories box, you should see a little pair of hyperlinks: [edit/delete]. Choose "edit."
PS - Your "memory" looks more like an exceptionally detailed biography than a "memory." I believe that "memories" are intended to be our personal recollections of the deceased person. The Biography section is not limited to computer-generated text ("John was born in 1912. He passed away in 1996"). Rather, the Biography is the place to document the events of the person's life, such as his military assignment. The complete texts of numerous letters might work better on a free-space profile.