The question "why would investigators show this sort of interest in an item of evidence" is a question only put by people unaccustomed to the procedure of evidence formation and collection called incidente probatorio. Which is not a forensic activity, but more like ritualized situation that provides the presence of lawyers, prosecutors and magistrates, experts of the various parties and officers as "screen". These people, in this case, where located in a van cabled to the video camera, talking and listening to voices on microphones. They mean exactly to "document" the collection of the clasp, because they are in a legal procedure legally depending on the attention of other people observing and recognizing the item.
The idea that was transferred to the clasp by touching the metal parts with gloves at certain instants is, well ... let's put the first question: transferred from where? Where did those gloves picked up Sollecito's DNA? Could you show me the source and the moment of the transfer? No source for Raffaele's DNA was found in the house. Even the door handles had been cleaned. It is not enough to assume they touched the metal part at a certain moment, you also have to assume they also touched something mysterious, never discovered, whishc contained some aboudance of Raffaele's skin cells.
Second: how likely is it to touch a microscopic source of DNA and transfer it with a touch? The same microscopic portion of the glove should touch both the source and the point of delivery, and the DNA must be solved in a liquid substance so can be "picked up", and also it must happen that casually this leaves the glove and is deposited on the new surface in that point. And the bra clasp showed dehydrated skin cells attached to the metal.
Why should I assume such a series of events? I will never consider all those events as reasonable. likely occurrence.