What is a tallit?
According to the Encyclopedia Judaica:
TALLIT (Heb. TyZt, pl. tallitot; Yid. tales, pl. talesim), prayer shawl. Originally the word meant "gown" or "cloak." This was a rectangular mantle that looked like a blanket and was worn by men in ancient times. At the four corners of the tallit tassels were attached in fulfillment of the biblical commandment of zizit (Num. 15:38–41). The tallit was usually made either of wool or of linen (Men. 39b) and probably resembled the abbayah ("blanket") still worn by Bedouin for protection against the weather. The tallit made of finer quality was similar to the Roman pallium and was worn mostly by the wealthy and by distinguished rabbis and scholars (BB 98a). The length of the mantle was to be a handbreadth shorter than that of the garment under it (BB 57b). After the exile of the Jews from Erez Israel and their dispersion, they came to adopt the fashions of their gentile neighbors more readily. The tallit was discarded as a daily habit and it became a religious garment for prayer; hence its later meaning of prayer shawl.Notice the highlighting in the paragraph above. It is probably unlikely that Jesus had such a prayer shawl or that the burial shroud was a tallit.