What do the parting words of the poet and her smile signify?

The poet’s parting words, “see you soon, Amma,” signify both her farewell to her mother and an effort to leave her with optimism and cheer. They also enable the poet to empathise with the sense of isolation faced by her mother in the old age.
Her smiles signify her helplessness at the face of her mother’s inevitable death. They express her love and concern for her mother along with the underlying pain and struggle that she undergoes in coming to terms with this bitter realisation.