Maybe I'm confused, but on the first day they do have the special welcome drink in the souvenir cup (just did it on the Wish in January and last summer on the Fantasy/Wonder). You can keep using it all week for refills. My understanding is you get a larger serving for the same price.
Sometimes they have washed the cup for me, sometimes they give me a new one, and one time...yuck. So, I do try to keep it clean between uses now, just in case.