Dr. King refers to peaceful protest when referencing the "majestic heights". He describes peaceful protest as meeting physical force with soul force, or the will to see that justice is enacted through nonviolent means. This is truly a difficult thing to accomplish in the face of brutal injustice, and is a majestic height to reach indeed. Dr. King proved that such heights could be reached, and that real progress toward equality could be made by nonviolent means.
Hester means that the letter has been on her for too long and too many people have seen it for it to just be taken off. The damage the letter has caused her has already been done.