Spoilers à frente:
The most information we can get from the book can be found in the General Features section of the hideout description, in the box titled "What the Redbrands know" (page 20):
The Redbrands have a handful of captives in a holding area "near the old crypts," which are guarded by skeletons (see areas 4 and 5).
This only tells us that the Redbrands are aware of the skeletons (it's their trap after all). However, it is likely that at least some of the Redbrands would know the command word as well, as the trap is positioned right in front of their prison, and the skeletons might otherwise interfere with prisoner transfer.
If this doesn't seem likely to you, there is at least one person in the hideout that is expected to know such things: Glasstaff himself. Though it is not strictly specified in the book, it is very likely that he's the one who set up the whole trap, and thus would know the codeword.
As for how could your PC-s find this out? Interrogation, persuasion, magical effects, and others. While getting information that you don't ask for in an interrogation seems unlikely, a particularly successful one could yield it. For instance, if your PC rolled an Intimidation check while interrogating and got a very high score, an NPC might be so scared that he starts spewing out everything he knows (possibly pissing his pants at the same time). Or a well worded Suggestion ("Lead us safely through the hideout") spell might prompt an NPC to divulge such secrets. It's even possible to make allies out of enemies, and an ally would be incentivized to keep his new friends safe from skeletons.
Como uma nota lateral: o livro de aventuras que você está usando é não é um livro de regras. É apenas uma sugestão de como jogar a aventura da maneira que o autor a imaginou. É permitido ao DM (e necessário, imho) adaptar a aventura de acordo com o andamento da campanha.
Aderir ao livro é útil para novos DMs que ainda lutam com todas as suas outras responsabilidades e não desejam adicionar histórias adaptáveis à lista. Mas o livro não era para ser um livro de culinária, portanto, naturalmente existem alguns buracos no texto que o Mestre precisa preencher. Isso também é uma boa prática, pois modificar o script inicial em reação às ações do PC geralmente leva a uma campanha muito mais agradável do que apenas seguir o livro.
Em resumo:
The PC's might not enter the skeleton room at all, at which point the keyword is irrelevant. It is also irrelevant in case the players stumble upon the room before gathering any information. But it's good for a DM to know it exists so he can throw it in at any point in the game where it would make the game more enjoyable (as a reward for a high roll, or even as a new plot point that enriches the original adventure).