Deborah,
Well, they weren't from or intended for Titanic's Smoking Room. Her tiles, visible at the wreck site, are blue and red. Olympic's were yellowish and white. That particular tile pattern went into numerous H&W-built ships, so the tiles that H&W found in their old office spaces one day and decided to sell as "Titanic" Smoking Room tiles could have been overrun on any number of production orders, not even necessarily Olympic's.
The tile is the correct pattern, but not the correct colour, for Titanic. Now, the best tie-in one can surmise is that the same tile used in Olympic could have been ordered for Titanic, but that someone changed the colour requirement after the tiles were produced. There's no evidence of this, though...it's just supposition on my part. I don't even believe that's what happened. Instead, I think that a bunch of tiles were made for some ship (which will forever remain unknown) and those that weren't used for the ship were laid down in some H&W administrative offices (which is quite sensible). Then along comes the wildly popular film, "Titanic," and somebody sees profit in those old tiles (a friend related a story where he was touring the shipyard either just before or right after the film's release, and happened across a stack of these old tiles in a storage area. When asked if he could take one as a souvenir, he was invited to take as many he liked), especially since they could ask about a 1500% markup (originally...looks like it's gone up since then). I see no need to invest in this item, even if it is a genuine tile from the period. Especially at those prices.
Parks