In the book, the color red symbolizes the struggles that cause strife in Henry and Clare’s relationship and make it hard for them to exist in the here and now, together. Alba’s ruby slippers build on this symbolism. They are a nod to the famous ruby slippers of film
The Wizard of Oz, in which the protagonist Dorothy clicks ruby slippers together to transport herself home from the magical world of Oz. In the context of Henry and Clare’s story, the slippers suggest Alba’s (and Henry’s) time traveling. Perhaps Henry bought them for Alba as a symbol of comfort to Clare to remind her that Alba will always return to her. But in order to return, Alba must first travel
away from Clare, making the slippers as much a symbol of Clare’s struggles and worries as a symbol of comfort. Perhaps this is what motivates Clare to agree—albeit reluctantly—to Henry’s request to let Dr. Kendrick study Alba.