I was surprised to find that the pronunciation of the word valet includes the final T. In the modern usage of the word, valet parking, we say the word as if it were a French ending.
Hearing the way they said it in the show, I wondered if the original word might be related to the word varlet, so I looked it up. And found the Online Etymology Dictionary does say the words are related.
"personal man-servant," 1560s, from Fr. valet, from O.Fr. valet, variant of vaslet "man's servant," originally "squire, young man," from Gallo-Romance *vassellittus "young nobleman, squire, page," dim. of M.L. vassallus, from vassus "servant" (see vassal). Modern sense is usually short for valet de chambre; the general sense of "male household servant of the meaner sort" going with the variant form varlet. First recorded use of valet parking is from 1960.Podictionary has an interesting post about the word, also.
The Macquarie Dictionary gives both pronunciations, and defines the word as:
noun 1. a male servant who is his employer's personal attendant, caring for the employer's clothing, etc.; manservant.It refers to the related word, varlet:
2. someone who performs similar services for patrons of a hotel, etc.
3. any of various contrivances, as a rack or stand, for holding coats, hats, etc.
–verb (valeted, valeting)
–verb (t) 4. to work as a valet for (someone).
–verb (i) 5. to work as a valet. [French, variant of Middle French vaslet. See VARLET, VASSAL]
noun Archaic 1. an attendant.
2. a page attached to a knight.
3. a rascal. [Middle English, from Old French, variant of va(s)let VALET. See VASSAL]