We only have Stowe's family members' testimony.
Scholars continue to describe the quote as "apocryphal", originating from the Stowe family but from neither Harriet Beecher Stowe herself nor Lincoln (although Stowe described Lincoln as funny, which would be consistent with such a joke). In the article Lincoln, Stowe, and the "Little Woman/Great War" Story: The Making, and Breaking, of a Great American Anecdote, Daniel Vollaro writes
Despite its popularity, however, the quotation is entirely apocryphal, emerging from within Stowe family tradition without any textual support or verification from the author herself. Most of Stowe's biographers have included some version of the quote, almost always scrupulously attributing it to its apocryphal origins. Many twentieth-century literary scholars, critics, and historians who reference the incident were not as careful as Weinstein to qualify the quotation with phrases like "allegedly said" or "is reported to have said."
The "" is a footnote that reads
In her 1937 biography Harriet Beecher Stowe (New York: Appleton-Century), 273, Catherine Gilbertson attributed the quotation to "family legend." Similarly, Forrest Wilson says it originated from a "family story" (Crusader in Crinoline: The Life of Harriet Beecher Stowe (Philadelphia, Pa.: Lippincott, 1941), 484. Johanna Johnston's account in Runaway to Heaven (Garden City, N.Y.: Doubleday, 1963), 357, ushers the reader into Lincoln's parlor along with Stowe and emotes: "the rest would be legend forever after, to Harriet and all her family." After opening her preface to her Harriet Beecher Stowe: A Life (New York: Oxford University Press, 1994), vii, with the quotation, Joan Hedrick writes that Lincoln "is said to have greeted" Stowe.
I did some more digging to try to find contemporary (or near-contemporary) accounts of the quote, to see where exactly in the Stowe family history it came from. Authors and Friends includes Fields' 1896 writing indicating that the first person in the family to repeat it was one of Stowe's daughters, presumably not long after the meeting. She found it out from an intermediate source - neither Stowe nor Lincoln:
It was left for others to speak of her interview with President Lincoln. Her daughter was told that when the President heard her name he seized her hand, saying, "Is this the little woman who made this great war?" He then led her apart to a seat in the window, where they were withdrawn from other guests, and undisturbed.
Now, Vollaro says that three of Stowe's family members were with her for the meeting: her daughter Hattie, her son Charles, and her sister-in-law Isabella. Charles apparently wrote about the quotation in his 1911 biography, but there is doubt as to whether he was actually at the meeting. Regardless, the quote seems to have been popularized - and perhaps invented - by - Stowe family members around the turn of the century. Unless we believe that Charles was present, there are no primary sources who have been recorded as confirming the quote.