Question

Whose terribly transient feet is the poet talking about what are they transient

Answer 1

The poet is referring to the feet of her mother. They are transient because her mother is not alive anymore. 

Answer 2

The terribly transient feet referred by the poet refer to his mother who is no more.

He recollects her memory with the photograph taken on the sands of the beach which they would visit during old times. The photograph of the footprints taken on the sand of the beach would be enjoyed by his mother.

The word transient refers to something which is short-lived and not permanent and here it refers to the mother’s feet.