Unidentified Bodies comparison with unrecovered body list?

My question is rather morbid, but was there any attempt to identify the unidentified bodies either interred or buried at sea, with the passenger list showing those not recovered or accounted for? I can only imagine what an unsavory job body recovery was, but how did they try to identify the ones they did find? Of the things found with the bodies, did White Star try to find possible relatives to give them to? Just don't understand why more wasn't done to discover more about the unidentified bodies. Thank you if you have any information.
From what I have read every body recovered was thoroughly documented. They documented height, weight, clothing, jewelry and personal effects found on the body. The problems with identification were with the condition of the bodies when they were found. The first of 4 ships ship to arrive at the scene to recover bodies was the Mackay Bennett on April 19th. This was 4 days after the sinking so the bodies were in the sea, decomposing and open to the sea life and elements all that time. She searched for an additional 7 days after that so some of the bodies she recovered were in the water for up to 11 days. Many of the bodies were in such bad condition that they were unrecognizable and only identifiable by the items found on them. Labels sewn into clothing with initials on them, initials on jewelry, names found on documents found in pockets on the bodies were all documented and used to aid in identification. Many bodies however, had nothing on them that could aid in identification and a physical description could potentially match any number of victims so it was virtually impossible to positively identify some bodies.

Doug Criner

The descriptions recorded for the unidentified bodies were pretty nonspecific, e.g., female, approx 5'-6'' tall, no identification papers, blue sweater, of possibly southern European extraction. Without modern forensic evidence, fingerprints, DNA, etc, it would have been difficult to match such descriptions to known missing. Decomposition and damage due to wave action provided more limitations.

Recovery, identification, and return of corpses might have been considered less important than today, and certainly less easy. But relatives of Benjamin Guggenheim, the millionaire tycoon, spent a considerable sum of their own money for an independent search for his body (unsuccessful). I suspect that there was an element of the public who thought that was a vain waste of money, even for a Guggenheim, no less - so, think what level of effort might have been expended trying to identify the body presumed to be that of a third class passenger or a stoker.