A delegation of Christian and Muslim leaders returned to the United States from Iran hoping that their six-day visit will improve relations between the two squabbling countries in a way that diplomatic channels have not. The four-member delegation, which included Cardinal Theodore E. McCarrick, retired archbishop of Washington, hoped to be accompanied on the return home on Sept. 19 by a pair of American hikers who were incarcerated by Iranian authorities on charges of espionage and of entering Iran illegally. The two men were finally released on Sept. 21. The trip was arranged by Search for Common Ground “to try and deepen the relationship between the two countries by direct human contact on the basis of religious leadership,” said William G. Miller, senior adviser to the organization. Cardinal McCarrick believed discussions among Iranian and American religious leaders would deepen trust where diplomacy has failed. “The political channel doesn’t do too well right now. There should be another channel. The other channel is the religious channel,” the cardinal said.