Simple it was made there. The selling of religious artifacts to the gullible was common. Nails from the cross, pieces of the cross and the ark, fingers, feet, and other bones of one saint or another. Pilgrims were always traveling to the holy land. Someone once remarked that enough pieces of the Cross had been sold to make up many crosses. The shroud probably originated there but was a medieval fake.
I'm not so sure it was made there, the first reported instance puts it in France, so I would guess either a European origin, or in Constantinople. Europe because in 1390 it was claimed to have been forged in France, or Constantinople because the city was famous for the manufacture of religious icons.
As to the pollen, from the few plants mentioned on Wikipedia that I checked, the range was Mediterranean, not just Judean. The article also claims that the sample could have been deliberately contaminated.
Items like pollen and blood stains do not help us, as these could have been introduced since the shroud was manufactured. For example, genetic material recovered from the shroud came from both men and women.
Having compared the image on the shroud to Christian art from 800 to 1600, the proportion of the head matches artistic representations of people, Jesus included. It is not an anatomically correct image according to the quick test I have done on myself.