As the detainee population decreased during the final years of the Obama administration — which sought, and failed, to shut down the prison and transfer the remaining detainees to a facility in the United States — the Pentagon has embarked on a building spree at the base. Last July it issued a callout for construction contracts worth $240 million. The month before, the Pentagon awarded a $66 million contract to a firm owned by a Cuban-American family to build a new school on the base for the children of people posted there for long periods.

Congress has not seriously questioned the merits of this buildup. During a House Foreign Affairs Committee hearing in March 2016, only one lawmaker argued that the United States should rethink its claim to the land. “This is in my mind something that could be well characterized as colonialism,” Representative Alan Grayson, Democrat of Florida, who is no longer in Congress, said during the hearing.

Might the Cubans be willing to allow the United States military to remain on the base under a new agreement similar to those that regulate the presence of American service members on foreign soil across the world? David Kohner, the chairman of the Maritime History Center at the United States Naval War College, thinks this is the right time to be raising that question, considering President Raúl Castro of Cuba is expected to step down next year.

“This is a difficult history, but history is what it is,” he said, emphasizing the need to move on from the terms of a lease signed in 1903.

Since the Obama administration began normalizing relations with Cuba in late 2014, the two governments have begun cooperating more closely on maritime security, migration flows, counternarcotics and law enforcement matters. Mr. Trump’s shift on Cuba, ostensibly on human rights grounds, is an aberration for an administration that coddles brutal autocrats abroad and contradicts the foreign policy philosophy Secretary of State Rex Tillerson outlined during a recent Senate hearing. “We are motivated by the conviction that the more we engage with other nations on issues of security and prosperity, the more we will have opportunities to shape the human rights conditions in those nations,” Mr. Tillerson said.

The American presence in Guantánamo has long been a thorn in the Cuban psyche, a reminder of an era of American domination that is taught early and often in Cuban schools.

Carlos Alzugaray, a scholar who served as a Cuban diplomat from 1961 until the mid-1990s, told me there had been discussions during his time in government about what the Cuban government could do to challenge Washington’s claim on the territory. For instance, Havana could seek an opinion from the International Court of Justice on the legality of the American presence in Guantánamo or submit a detailed diplomatic note demanding the return of the territory.