What is the mark on the back? There is a lot of stuff out there called Limoges that is not hard fired porcelain.
If it is hard fired porcelain, it won't stain.
Perhaps that's the way the pattern was meant to be?
At any rate more info and a picture or 2 might help solve your problem.
Linda C

I think I would try using a little baking soda on a wet rag. It won't scratch, and it just might remove the stain, especially if it is nicotine. It sounds like a lovely set of dishes, sure hope you can rejuvenate them. Luvs

Linda,

Sorry, I didn't think to take photos while we were packing and now everything is packed away in storage. I looked online to see if I could find some examples of the markings that were on the back, but I didn't see any. Oh well.
I know the staining is not part of the pattern because it isn't on all of the pieces, and my MIL remembers this china from her teenage years and says it wasn't like that back then. But thank you for responding and trying to help. :)

Luvstocraft,

I will definitely try that when we unpack it. Thanks for the suggestion. :)

Stumpy

Just bumping this up. Stumpy, have you tried cleaning the china yet with the baking soda? I would never have guessed that nicotine could do that! Wow.

Nicotine CAN'T do that...tobacco stains will wash off easily with Dawn or 409 or baking soda...there is something else at hand.
And because the OP says it's Limoges which is a hard fired porcelain type ware, it won't stain and discolor in the body of the ware.
So, either the ware is not Limoges porcelain, and is a softer bodied ware that crazes and allows stains to penetrate or the "stain" is not a stain at all but part of the pattern.
Linda C

I just found a Johann Haviland set of dishes in the same condition at inlaws estate. Top two in every pile as well as all the teacups were actually gummy with smoke. It washed off with a nylon scrubbie and Dawn. Sure baking soda would have worked too. Sandy

Dish Soap and Baking Soda took the discolouration right off. It was just dirt.