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The phrase dusty answer designates an unhelpful or bad-tempered reply.
It is, for example, the title of the first novel of the British author and translator Rosamond Lehmann (1901-1990): Dusty Answer was published in 1927.
This sense of the adjective dusty (i.e., uninteresting, unsatisfying) is related to corresponding uses of the noun dust, as in dry as dust, meaning: completely lacking in interest and stimulation.
The earliest occurrences of the phrase dusty answer that I have found are as follows, in chronological order:
1-: From Modern Love, a narrative poem of disillusionment, by the British poet and novelist George Meredith (1828-1909), published in Modern Love and Poems of the English Roadside, with Poems and Ballads (London: Chapman & Hall, 1862) [50, page 82]:
Thus piteously Love closed what he begat:
The union of this ever-diverse pair!
These two were rapid falcons in a snare,
Condemn’d to do the flitting of the bat.
Lovers beneath the singing sky of May,
They wander’d once; clear as the dew on flowers:
But they fed not on the advancing hours:
Their hearts held cravings for the buried day.
Then each applied to each that fatal knife,
Deep questioning, which probes to endless dole.
Ah, what a dusty answer gets the soul
When hot for certainties in this our life!
2-: From Lessons for the Day (London: E. W. Allen; Manchester: John Heywood) of Thursday 23rd November 1882—on Pessimism, delivered before the South Place Religious Society, South Place, Finsbury, London, by the U.S. abolitionist, clergyman and author Moncure Daniel Conway (1832-1907) [No. 8, page 89]:
As one has said, man gets dry and dusty answers when he asks for realities. For while man has become scientific the long theologic habit which evolved him still lingers.
3-: From A Library of the World’s Best Literature Ancient and Modern (New York: The International Society, 1897), edited by the U.S. author Charles Dudley Warner (1829-1900) [Vol. 35, page 14014]—the following is about the U.S. poet and novelist Elizabeth Barstow Stoddard (1823-1902):
In both her poems and her novels is reflected her sense of the beauty and aloofness of nature: of the “dusty answers” to the clamors of impetuous human souls.
4-: From An Englishwoman’s Love-letters (New York: Doubleday, Page and Co., 1900), by the British author Laurence Housman (1865-1959) [Letter 54, page 227]:
Beloved,—We have been having a great day of tidyings out, rummaging through years and years of accumulations—things quite useless but which I have not liked to throw away. My soul has been getting such dusty answers to all sorts of doubtful inquiries as to where on earth this, that, and the other lay hidden. And there were other things, the memory of which had lain quite dead or slept, till under the light of day they sprouted back into life like corn from the grave of an Egyptian mummy.
5-: From a review of Sister Teresa (London: T. Fisher Unwin, 1901), a novel by the Irish author George Moore (1852-1933)—review by ‘Lounger’, published in the East Anglian Daily Times (Ipswich, Suffolk, England) of Monday 15th July 1901 [page 5, column 2]:
It will be seen that Mr. Moore’s solution of the problem of Evelyn’s life is not cheerful, but I do not see how it could have been otherwise. It is too often but a “dusty answer” that we get in these matters, and those who suppose that Evelyn’s repentance should have brought immediate happiness, can have only a superficial understanding of the word repentance.
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