The last patients have been discharged from the Central Park field hospital run by Samaritan’s Purse, the evangelical organization led by the Rev. Franklin Graham. Its white tents will soon be dismantled and sent to new makeshift coronavirus wards as far away as Ecuador and Alaska. Doctors and nurses from Samaritan’s Purse treated more than 300 New Yorkers after Mount Sinai Health System invited the group to the city at the height of the pandemic, but its work has been dogged by controversy since it began. In an interview on Thursday amid empty tents, Mr. Graham said the decision to leave New York had been motivated by falling infection numbers, not by politics. But he expressed pique at his critics, who he said had been “a distraction” from the work of saving lives. The presence of Samaritan’s Purse in one of the country’s most liberal cities kindled a culture war in New York’s coronavirus response, drawing criticism from elected officials, religious leaders and L.G.B.T. groups unnerved by Mr. Graham’s past statements on Islam and gay issues, as well as by a requirement that the organization’s employees be Christians who oppose same-sex marriage.