Ten days after the Whittier dinner, MT wrote the three authors whom his tramps had impersonated to offer his "repentance" for his speech. As you can see from the article below, from a paper in the midwest that is reprinting an article from a paper in Boston, MT's apology was deemed as newsworthy as his original offense. The paraphrase of MT's letter is essentially accurate: in the letter MT had said that "I do not ask you to forgive what I did that night, for it is not forgivable; I simply had it at heart to ask you to believe that I am only heedlessly a savage, not premeditatedly."

You can read the entire letter (dated 27 December 1877) at the Mark Twain Project's ONLINE ARCHIVE.

From the Milwaukee Daily Sentinel
18 January 1878

Mark Twain Apologizes.

    Boston Herald: Mark Twain is characteristic, even in an apology. His speech as a droll at the Whittier banquet was unfortunate, and none felt it to be so more than the humorist himself, but his apology to the great lights of our literature, to Longfellow, and Whittier and Emerson, and Holmes, is so utterly abject and forlorn, that all will forgive Mark from the bottom of their hearts, and particularly those whom he caricatured. We have not the text of his letter at hand, but understand that he said to them in substance that he was a fool, that he knew it, but that God made him a fool, that he was God's fool and couldn't help himself, and that they ought to have a little compassion on him for God's sake, if not for his own. If there is any apology in existence which is more searching than this, we should like to know where it is to be found.