What is the term for an offeree's response that rejects an offer by varying its terms?

The term that refers to an offeree's response that rejects an offer by varying its terms is a counteroffer. A counteroffer occurs when the original offer is not accepted as presented; instead, the offeree proposes different terms, effectively creating a new offer. This means that the original offer is void, and the original offeror must then decide whether to accept the new terms or not.

Understanding the concept of a counteroffer is crucial in contract law, as it highlights the principle of mutual assent and negotiation between parties. A counteroffer initiates a new set of discussions, allowing both parties to renegotiate terms until they reach an agreement that satisfies both sides.

The other terms listed are distinct from a counteroffer. For instance, a counterclaim is typically used in legal disputes to assert a claim against an opposing party. A counterproposal might suggest terms but doesn't necessarily reject the original offer outright, which can create confusion in the negotiation's intention. A counterargument pertains to presenting opposing views in a debate, which is unrelated to contract formation. Therefore, the concept of a counteroffer best captures the scenario described in the question.