Is informing someone that another person described them as a liar based on a specific incident considered backbiting, and what is the correct action in such a situation?

Backbiting (namimah) is the disclosure of what one dislikes to be disclosed, whether verbally, in writing, symbolically, or by اشاره (implying), and whether what is conveyed consists of words or actions, and whether it is a defect or something else. It is the divulging of secrets and the tearing of the veil (of privacy) concerning what one dislikes to be revealed. It is forbidden and a major sin (kabirah). The hope that a liar might retract his lie does not permit it. Rather, one can highlight the danger of lying without resorting to backbiting. Backbiting may be permissible in specific cases.