Action by Christians Against Torture (ACAT) was speaking after the group, deemed safe for release by US security services, were sent to the United Arab Emirates.
Twelve of the prisoners were Yemeni nationals and three were Afghans.
President Barack Obama has vowed to close Guantanamo Bay during his administration, which comes to an end this January after seven years, and ACAT says this is the "best chance he's ever had" at accomplishing that.
The Pentagon says 61 detainees now remain at Guantanamo, which was opened in January 2002 to hold foreign fighters suspected of links to the Taliban or the al-Qaeda terrorist organisation.
It has received criticism for refusing inmates access to a fair trial and there are claims prisoners have been tortured there. Others say the prison is necessary to make sure potentially dangerous terrorists are out of mainland US prisons and unable to commit crimes.
British resident Shaker Aamer (below) was held without charge in Guantanamo Bay from 2002 to 2015 after being captured by bounty hunters in Afghanistan in 2001, and claimed he was tortured during his detention there.
Speaking about President Obama on Premier's News Hour, Derek Lewis from ACAT said: "He's been trying [to close Guantanamo Bay] for a very long time... but there seems to be a hard core of resistance in Congress.
"If they are dangerous, if they are terrorists, prove it - prove it in a court of law. This is what happens internationally. Why not in the United States?"
Speaking to Premier, Philip Gardner, an international politics expert, said: "I do think it's very important that whoever the next president is, they realise the damage that Guantanamo Bay does to America's image around the world.
"The United States is a country with a strong tradition of civil liberties and Guantanamo Bay stands apart from that tradition."
Listen to Premier's Antony Bushfield speaking to Derek Lewis on the News Hour:
Listen to Premier's Aaron James speaking to Philip Gardner:
