Okay, so, the first story, "The Things They Carried," is definitely about the war. It tells us about all the things that soldiers carry. (See "What's Up With the Title?" for more on this.) The book ends, however, with an oddly fractured story that's split three ways in time. Part of the story—about Timmy and Linda —takes place before the war began. Part of it—the piece about confronting death and dead bodies in Vietnam—takes place during the war. And the last part—about the need to write about all these things—takes place after the war.
All of these stories focus on death as well as the role of stories and memories in coping with death.
In the end, as O'Brien told us in "How to Tell a True War Story," a true war story isn't about war:
It's about love and memory. It's about sorrow. It's about sisters who never write back and people who never listen. (How to Tell a True War Story.106)
Given this quote, of course the final story in the book focuses on all those things instead of on war. We have Linda dying before the war and Curt Lemon, Kiowa, and Ted Lavender dying during the war. And we have O'Brien from all three times—pre-, during, and post-war—desperately trying to bring the dead back with lots of memories and lots of stories.
And as for the "sisters who never write back and people who never listen," O'Brien really means civilians, and the lack of communication between soldiers and civilians. That lack of communication isn't really a part of the concluding story—it's far more concerned with the love and sorrow and memory bit we've already mentioned. Instead, the lack of communication comes in later, when we've actually finished that last story. Yeah, it's tricky.
When readers finish a book, they instinctively judge whether or not it was worthy of being read. Basically, after finishing The Things They Carried, we have to decide whether or not O'Brien was able to communicate with us successfully—whether he really got to us.
It all comes back around to the epigraph—do we buy into his story-truth because he's a soldier, and must know what's true in wartime better than we do? Or do we decide not to trust him, not to listen—to figure it's all made up? A thought-provoking ending, right?