Witch
About
Very little about her past is known, but she answers a client that she, too, had lost someone important. Later, she muses to the delivery man that sometimes she bases her self-worth on the value of the objects she receives from customers as payment. On another occasion, a genie notes that the witch is magically bound to the restaurant and can't leave it.
The witch is heavily implied to be the reincarnation of Princess Kaguya. In one chapter, the witch remarks that she and the cat cannot return to the moon, and in another chapter her past incarnation asks the past incarnation of the delivery man to bring her "a cowry shell born of a swallow" (a request repeated by the witch when she meets his present reincarnation).
The black cat who accompanies the witch is also hinted at to be the reincarnation of Taketori no Okina, the bamboo cutter who finds Princess Kaguya in a bamboo stalk.