I think the case was that, far from the British raising objections, the US government sued the UK for reparations because HM government had knowingly allowed a warship to be built for a combatant nation in defiance of international law (Britain supposedly being a neutral country). The British government supported the Confederates because of the valuable cotton trade which made the mill owners of Lancashire very rich.

The case dragged on for years (until about 1893 I think) but the US was eventually awarded $15.5m.

As Lighter says, passengers and crews of merchant ships were removed before the ship was fired. Kell mentions people being brought aboard the Alabama in his book.