To me, the biggest and most important symbol of the story are the two flowers that Weena puts in the time traveller's pockets as a sign of her love for him and as a symbol of the burgeoning relationship that is growing between them. These of course function in many ways in this excellent story. They act as proof that the time traveller is speaking the truth, however at the same time they also are explicitly referred to at the end of the novel by the narrator as being symbolic of a hope for the future:
But to me the future is still black and blank--is a vast ignorance, lit at a few casual places by the memory of his story. And I have by me, for my comfort, two strange white flowers--shrivelled now, and brown and flat and brittle--to witness that even when mind and strength had gone, gratitude and a mutual tenderness still lived on in the heart of man.
The stories that the time traveller tells the narrator and his friends about the future of humanity are disturbing in the way that they present our evolution, but the flowers are richly symbolic of the way that however we change in the future, we still manage to retain the capacity to love and develop relationships.