Middle English toile, toille, borrowed from Anglo-French toille, probably variant of tieule, teulle, tuille "terra-cotta roofing tile" (the piece of armor so called from its resemblance in shape), continental Old French tieule, tiule, going back to Latin tēgula — more at tile entry 1
The French word in this sense is apparently only found in the text of an account of a tournament held in 1467 between Lord Scales and the Bastard of Burgundy, preserved in British Library manuscript Harley 4632. The English version of the same account provides one of the two citations for the word in the Middle English Dictionary. The text is printed in William Bentley, Excerpta Historica, or, Illustrations of English History (London, 1833), p. 181. No meaning relating to armor is recorded in dictionaries of medieval French (Tobler-Lommatzsch, Godefroy, Dictionnaire du moyen français, Anglo-Norman Dictionary).