What do we call the religious movement that aimed to enforce Church rules and independence from kings?

The story behind the answer

Led by Pope Gregory VII in the 11th century, this papal program sought to free the Church from secular control by banning lay investiture, combating simony, and enforcing clerical celibacy—asserting that only the Church could appoint its clergy and set its rules, independent of kings.

Its hard line sparked the famous clash with Emperor Henry IV—excommunication and the Walk to Canossa (1077)—and helped build the foundations of medieval papal authority and canon law. For context: the Cluniac movement was a monastic renewal, the Investiture Controversy was the conflict this agenda triggered, and the Conciliar movement came much later, aiming to place general councils above the pope.