Henry is courting Anselm because he needs…

Henry is courting Anselm because he needs his support for the security of his claim to the throne; Anselm could have thrown his support behind Henry's elder brother instead.

When Anselm returns, Henry requests that Anselm do him homage for the Canterbury estates and receive from him investiture in his office of archbishop.

The papacy had recently banned clerics doing homage to laymen, as well as banning lay investiture; thus had started Anselm's conflicts with Henry.

Henry refuses to relinquish the privilege possessed by his predecessors, and proposes that the matter be laid before the pope.