The most telling argument against the shroud being associated with Jesus burial is the way Jesus burial with a face cloth and linen clothes being wound around Jesus body with a large quantity of spices and ointments being applied. (John, chapter 20)
Whatever the shroud is and where it came from it is not what the Bible describes as the clothes that covered Jesus.
"Then he (Joseph of Arimathea) bought fine linen, took Him down, and wrapped Him in the linen. And he laid Him in a tomb which had been hewn out of the rock, and rolled a stone against the door of the tomb." Mark 15: 46 New King James VersionIn the original Greek, that verse says that Joseph of Arimathea purchased a fine Sindon, a shroud, not strips of cloth. The linen of the Shroud is a very fine Linen, hand woven, that represented about two months worth of labor. The idea of "winding" cloths around the body is a confabulation resulting from confusing Egyptian burial techniques with those of the Hebrews. First Century Jews did not bind their dead in mummy like wrappings... they did not embalm, or wrap them tightly in yards and yards of linen strips. Burials were fairly simple rituals requiring washing the body, annointing with oils, and packing around the body with herbs and spices. Extant documents show that Jews buried their dead with a shroud, strips of cloth that bound the ankles and wrists to prevent them from flopping, and another strip around the head, under the jaw, to keep the mouth closed. Exhumations of 1st Century Jewish burials show that the shroud is not inconsistent with Jewish burial customs.
Just because something isn't explicitly mentioned in the Bible, doesn't mean that it doesn't/didn't exist.
The image on the Shroud conforms to the Jewish burial practices of Jesus' time.
John chapter 20 is very interesting.
John 20A logical inference, given their knowledge.1 Early on the first day of the week, while it was still dark, Mary Magdalene went to the tomb and saw that the stone had been removed from the entrance. 2 So she came running to Simon Peter and the other disciple, the one Jesus loved, and said, "They have taken the Lord out of the tomb, and we don't know where they have put him!"
3 So Peter and the other disciple started for the tomb. 4 Both were running, but the other disciple outran Peter and reached the tomb first. 5 He bent over and looked in at the strips of linen lying there but did not go in.
It appears that John didn't say anything, so we can assume that he did not disagree with Mary's conclusion.
6 Then Simon Peter, who was behind him, arrived and went into the tomb. He saw the strips of linen lying there, 7 as well as the burial cloth that had been around Jesus' head. The cloth was folded up by itself, separate from the linen. 8 Finally the other disciple, who had reached the tomb first, also went inside. He saw and believed.What did John see and believe? That Jesus had risen from the dead? Why would he assume that? In fact, the very next line states:
9 (They still did not understand from Scripture that Jesus had to rise from the dead.)John had already seen the "strips of linen." But he didn't see "the burial cloth that had been wrapped around Jesus' head" until he entered the tomb. Why would seeing a plain white burial cloth cause John to "see and believe"? The disciple's behavior is very puzzling, and very difficult to explain given the information provided in John 20 alone.
The existence of the Shroud provides a satisfying explanation for the disciples' behavior. An image of Jesus on the cloth would have indicated to Jesus' disciples that something miraculous had occurred, and it would explain their behavior upon entering the tomb, as recorded in John 20.