"Het meisje" is an exception, because it is actually a diminutive that is derived from "de meid". All diminutives (ending on -je) are het-words. For example, it is "het vrouwtje", "het jongetje" and "het mannetje". Later on in the tree you'll learn how to form these.
Over time, the diminutive "meisje" has come to largely replace the original "meid" as the standard word for 'girl'.
And for me, I really don't hear the "s" at the end. Is there some pronunciation variance because the "s" is at the end? It sounds like something that happens with Korean words (where "ch", "t", s", and "ss", for example, all sound like a short "t" at the end when there is no following word).