Badabinski , 3 days ago

Not trying to be pedantic, but you recover the body once someone is dead. Rescue specifically means that you're trying to get to a person before further injury or death can occur. Recovering someone's remains is done almost purely out of respect for our need for burials and closure. It's a really solomn and respectful thing that's not to be taken lightly, so recover is absolutely the right word to use here.

Source: I did some search and rescue training as a kid.