The apron and rag seem to suggest an alternate ending where E.T. gives up on trying to leave Earth and gets into bartending.
A 1982 bar poster produced by Coors, in which lovable alien E.T. The Extraterrestrial leverages his famous catchphrase to encourage patrons not to drive home drunk.
While information about this poster’s designer (or design process) is hard to come by, it’s worth noting that Coors beer is featured in the film; specifically in the pivotal scene where E.T.—blasted in the middle of the day after finding a pack of Banquets in the fridge—has the idea to “phone home” that drives the rest of the movie.
ITC’s Italia Bold is used for the entire poster, including the tiny copyright info at the bottom. It’s a very classy early-80s pick that somehow seems perfect for a poster featuring both a cozy-looking wood-paneled bar interior and a space alien.