Final answer:
Hugh of Cluny reminded Pope St. Gregory of the papal tradition of mediating political disputes and asserting spiritual authority over temporal leaders, which includes the power to grant pardon.
Step-by-step explanation:
The longstanding tradition that Hugh of Cluny reminded Pope St. Gregory of, as he hesitated in granting pardon to Emperor Henry, is rooted in the papacy's historical role in mediating between political powers and asserting spiritual authority. This tradition includes the negotiation of mutually beneficial relationships with kings, as seen with Gregory the Great, and the expansion of Christian missionary work. Pope Gregory VII, in the 11th century, continued this tradition by asserting the pope's authority over the appointment of church officials during the investiture controversy with Holy Roman Emperor Henry IV. The conflict reached a resolution when Henry ultimately sought forgiveness and was pardoned, partly stemming from the pope's spiritual power over temporal leaders, a concept influenced by documents like the Donation of Constantine.