The world is filled with these 'remnants'. One visit to the Holy Land, Jordan, Lebanon, Syria and all the other countries in the Middle East is in order.
This is why it is totally unprofitable and undesireable to search for them or even engage in discussion about them.
There is no profit made from the Shroud of Turin or the Sudarium or any of the other relics left behind by our Lord and His apostles. They serve only to justify what Scripture tells us. Remember St. Thomas? He wasn't in the Cenacle when our Lord appeared to the disciples. He said that unless he placed his hand on the wounds of Christ, he wouldn't believe. Then Christ appeared. The world is filled with "doubting" Thomases.
But then, some seem to need holy relics and aids to worship in order to feel something or other about God.
No one needs relics to believe. A relic is a tangible connection to the holy person. On Good Friday, christians from all around the world stream into Jerusalem and walk the same route that our Lord did on His way to Calvary. These believers don't need the exercise; they do this out of love, affection and great humility. Yes ....it takes great humility to place ourselves on the same path taken by Christ. That is why Catholics pursue a 40 day period of fast and abstinence, to suffer along with our Lord who gave His life for our salvation. He didn't suffer for Himself; He didn't need to. He suffered for you and me, so that we would be saved. What an awesome gift He gave us that day.
Humility and great courage and strength. One thing I never realized as a child was how followers of The Way are still cursed and mocked just like our Lord.
I think it is high time the Eastern and Western Churches unified. We are all brothers in Christ.