An Etymological Dictionary of the German Language/Schleier
Schleier, m., ‘veil, pretence,’ from MidHG. sleier, earlier variants sloier, slogier, m., ‘kerchief, veil’ (the MidHG. term floier is curious); comp. Du. sluijer, MidE. sleir. MidHG. sloier, first recorded in the 13th cent., is certainly a borrowed term; the assumption that it was introduced by the Crusaders from the East leads to no definite result. Perhaps it is connected with OIr. sról, ‘silk.’