They would immediately try take legal action against the American administration through any and every international court available. Having been detained without sufficient evidence there is a case to answer, the US and their cohorts (let us not forget that several governments including ours in the UK have been shown to be complicit in rendition actions that deliberately circumvented international law) can't try ignore the issue with the "enemy combatants" and other such reasons without looking like complete hypocrites given how loud they shout when someone they care to defend is detained without what they consider to be sufficient evidence (Iran holding several naval officers for instance). Even more embarrassing: some of the people they are refusing to let go home to face/demand their own country's justice are American - they don't even want their own legal system anywhere near this.
tl;dr: Just letting them go would certainly not be cost free, financially or in terms of local and/or international reputation.