Answer and explanation:
Mr. Dodd, writer of the play, is correct in emphasizing that no clothes of Ninja Turtles were worn in ancient times, although sending someone home for a mistake as simple as that seems to be a bit extreme.
When a historical period is artistically represented, it is always sought to bring to reality all that is pertinent to that period, to the smallest detail. Whether from customs, beliefs, ways of acting in certain situations and, obviously, the outfits that were used at that time. All these details must be properly taken care of and respected so that the play is, at the end, a success.