Source?
The provenance of ANY relic nearly 2000 years old would be expected to be imperfect, and the Turin shroud is no exception. No doubt before it landed in Constantinople (one of the 5 historic centers of ancient Christianity) it would presumably have been passed on to various faithful disciples, and given the times....not have been always recorded.
One physical clue, that has never been explained (and there are many) is the presence of Palestinian pollen on the cloth...of a kind that went extinct after the 1st Century.
The Shroud has been called THE most studied object from antiquity. Various different scholarly papers have been written concerning its provenance—before the 1300s, and, the evidence is shadowy, but, it is there too. If you are really curious you can look it up—much of the evidence is openly available through the Internet.
I recall reading some article that there is a very early (pre 12th C.) description that accurately describe the current shroud—and these are long before the radio carbon dating from one place (provably a patch...) showed 13th C. origin. I believe they even have medieval miniatures paintings of the cloth, BEFORE the 13th C.