The memorial to John Andre that Benedict and Peggy Arnold view is actually the case used to return his remains to England (as indicated by the writing on the side). He was buried in New York following his execution, but his remains were repatriated to England (in this case) in 1821, so Benedict Arnold (who died in 1801) could not have viewed this box.
However, there is a memorial to Andre in Westminster Abbey, placed there in 1782 expense of King George III, and is as described in the episode. Benedict and Peggy Arnold did visit this memorial in their lifetimes. (Andre's remains were buried in the Abbey after the repatriation, near this memorial.) Westminster Abbey still has possession of the case from the United States as well.
However, there is a memorial to Andre in Westminster Abbey, placed there in 1782 expense of King George III, and is as described in the episode. Benedict and Peggy Arnold did visit this memorial in their lifetimes. (Andre's remains were buried in the Abbey after the repatriation, near this memorial.) Westminster Abbey still has possession of the case from the United States as well.