I call your attention to this careful piece, The Castle of Ray-sur-Saône: Othon de la Roche and the Shroud of Turin by Mario Latendresse
The hypothesis that Othon de la Roche acquired the Shroud of Turin, during the conquest of Constantinople in 1204, has been proposed for many centuries….
In summary, there is no known family tradition supporting the presence of a shroud of Christ at the castle of Ray-sur-Saône, neither in the family archives. There is also no family tradition or document supporting the authenticity of the coffer, still on display at the Castle, which would have been used to transport a shroud of Christ. It is still to be determined who in the Salverte family labeled and placed the small coffer on display.