… I see the confusion.
The word “recover” has two meanings: an intransitive one in the sense of “heal” (which is what you understood – for example, “the soldier recovered quickly from his wounds”) and the other in the sense of “retrieve, get back” (which is what is meant in the extract – for instance, “they recovered the lost treasure”).
The “operation” in question is not a surgical one, but a body retrieval mission.
Hence, the person had already died, and they were on a mission to get his body back.
Hope this helped!