Phantom means ‘a spirit of a dead person which visits the living in the form of a person or animal’. Here, the she-monkey was gifted to Pia by her uncle from Chile. The she-monkey stayed as a pet with Pia and her family for a short time.
Pia got emotionally attached to her. Pia did not want to part with her, but for certain reasons, Pia’s elders sent the she-monkey back to the jungle of South America from where she was brought. A spirit usually makes its presence feel for time being and does not stay back for a long time.
In the same way, the she-monkey – Pepper – stays with Pia and her family for a short time creating emotional bondage with them, and then she leaves, therefore the she-monkey is called Phantom.