What type of reply is characterized by its sharpness and wit?

The term that fits the description of a reply characterized by sharpness and wit is repartee. Repartee refers to a quick, witty response or exchange of remarks typically marked by humor and cleverness. It involves not just the cleverness of the words spoken but also the timing and context, wherein the reply serves as a form of verbal sparring, showcasing the speaker's intelligence and eloquence.

In contrast, the other options do not align with the essence of a sharp and witty exchange. Retaliation suggests a reaction to an offense, often rooted in negativity or conflict, rather than a playful or humorous exchange. An invitation is a request for someone to join or participate, lacking the sharpness or wit characteristic of repartee. Debate implies a formal argument or discussion with structured points rather than the quick and clever banter that defines repartee.