Volyova at first thought the splinter was from Khouri's soldiering days, carelessly left in place by Chasm City's medics. However this strikes her as odd and she keeps it for later analysis.
After a description of Khouris "recruitment" in Chasm City (Chapter 20), Volyova believes it to have been planted by Manoukhian and that (Chapter 21): "If [..] this was Manoukhian's doing, it may tell us something about the Mademoiselle. Perhaps even her identity."
She also points out the oddities of the metal and the unique stress patterns that had been imprinted on it after manufacturing. A later analysis reveals that the splinter must've come from the contact vessel used at Lascaille's shroud. This was the message Manoukhian tried to convey by placing the shard into Khouri's skull: The Mademoiselle was Carin Lefevre, who had survived the incident at Lascaille's shroud and secretly returned to Chasm City (although not quite herself).
'Svinoi,' said Triumvir Ilia Volyova, because now there could be no doubt.