I feel it should be recovered. The reason I feel it should be recovered is because we should be able to honor those people who died. It always help to envision some one from your past if you have something tangible to see. (and feel in the case of family)
I know I personally feel better being able to see things from my parent's lives now that they are gone. I try to imagine their feelings, hopes, and dreams from that particular object.
If you were a family member of one of the passengers on the Titanic; wouldn't you wish to see something they had owned?
Try to look at this from the perspective of the families whose ancestor was on this ship.