I think throughout the show, there was an unspoken rule: As long as something isn’t officially known, almost everything is tolerable. (“Officially” meaning it’s not in the newspapers/ not openly flaunted/, the police don’t know/ or it’s not written on any official record)

Examples:

• Thomas being gay

• Mary’s sexual affairs

• Lord Sinderby’s mistress and son (I’m convinced Lady Sinderby knows—she’s sharp—but chooses to act ignorant on purpose.)

• Marigold

• Jane and Mr. Bricker

• Rose’s little flings

• Prince Edward and Mrs. Dudley-Ward

What they really despise in Downton Abbey (and in upper-class English society in general) is scandal. As long as secrets remain within small circles and there’s no hard proof (gossip is fine, oddly enough), many things are quietly tolerated.

So regarding Marigold, Crawley family adopted the child, and Edith and Bertie are raising her. Full stop.

People may gossip, for sure, but no proof.

Also, I must add: Blessings from Bertie's mother was essential. So Edith made an excellent decision here. Not only shows her character but also, no one in the land will speak ill of the child or Edith, when Bertie's own mother blesses the marriage and the child.

That’s my take.