This type of situation is often referred to as Hobson's choice (or Hobbs' choice).
It's from Thomas Hobson (1544-1631), a livery stable owner who offered customers the choice of either taking the horse in the stall nearest the door, or taking none at all (to make sure his best horses didn't get overused). Effectively, the "choice" was just take it or leave it.
Thus some people will say the expression implies your only choice is to accept or reject a single option on offer. But in my experience it's also commonly used where superficially there are two or more actual choices available, but all except one are manifestly unacceptable. That's to say, it can be used in situations where there's the illusion of choice, but only one is option is practical.
The best term I can think of for the "fake" alternative is bogus (or sham) choice/option/offer. I don't see that "decoy" fits very well, because usually a decoy is something you're intended to fall for.