This is a common occurrence in French when two vowels come together after an inversion. Coûte pronounced carefully in French is coo-tuh (the final e has the sound somewhere between "uh" and "er" in English). And to the French coot-uh-eel sounds awful. So they add the "t" between uh- and -eel to make coo-tuh-teel. The reason for the choice of t is that many verb endings in the third person end in t anyway, so with the inversion, the elision automatically makes a t sound before the beginning vowel of "il(s)", "elle(s)" and "on." For example: Sait-on? Vont-ils? Connaissent-elles? You see that all of the verbs have a t in the end. So when there is a missing "t" in the verb form of the other conjugations, a t is added for phonetic ease of pronunciation.