Let us remember that this incredible story allows us to see the dying thoughts and cares and concerns of a woman who is thinking about preparing herself for death. She has so many things that she wants to sort out before dying, and one of these things is the box of letters in the attic that your question refers to. Let us note what the text tells us about this box of letters:
The box in the attic with all those letters tied up, well, she'd have to go through that tomorrow. All those letters--George's letters and John's letters and her letters to them both--lying around for the children to find afterward made her uneasy. Yes, that would be tomorrow's business. No use to let them know how silly she had been once.
Thus we can see that the letters in the box are from her former lovers, George and John. Granny is thinking about them because she doesn't want her children to ever see those letters and see a different, more romantic side from the stern, indominatable mother who shows herself in this story. It is interesting that what dominates this tale is the lingering hurt that George caused Granny Weatherall when he jilted her. Her reluctance for anyone else to see the letters from this time likewise indicates the way that she tries to keep this deep wound secret.