The phrase "right of offset" refers to a legal ability to deduct obligations owed to one party from obligations owed by that party to another. Some synonyms for this phrase include setoff, counterclaim, and cross-demand. Setoff and offset are often used interchangeably to refer to the same concept of deducting one claim from another. Counterclaim refers to a claim made by the other party in response to the original claim. A cross-demand is a similar concept to setoff, as it involves offsetting obligations owed in opposite directions. All of these terms are commonly used in law and finance to describe the ability to offset debts and obligations against each other.