The phrase "a slight that" is not correct and does not convey a clear meaning in written English.
It may be intended to refer to a minor insult or offense, but it lacks context to be effectively used.
Example: "She took it as a slight that he didn't acknowledge her at the meeting."
Alternatives: "a minor insult" or "a small offense".
It was a slight that started a cold war between the stars that has tempered with time.
But notes he left at his home — where he lived with his wife, Marie, and their three children — said he was distraught about a slight that had occurred more than 20 years ago.
According to his wife, Laura, the first sign of discontent was his discovery that his salary payments were only about half of what Justo said Obaid had offered him – a slight that was compounded when he learned that the promised multimillion-pound bonus would be considerably less than that – more like six figures than seven.
Only in that way can one learn whether a patient has taken his analyst's mistake as a slight that has offended and angered him, or as a sign of weakness that allows him to feel superior and even triumphant, or as a welcome excuse for anger, etc.
As children they played together and Redmond's father, Wat, now an ailing old man, showed favoritism toward Laidlaw at Redmond's expense, a slight that causes Redmond to resent Laidlaw.
In "The Deep Blue Sea" Hester, the beautiful wife of a judge, falls hopelessly for a younger ex-fighter pilot who forgets her birthday, a slight that plunges her into suicidal despair.
That is certainly a slight concern that should be remedied later this year.
I feel that you have a slight problem that is getting in the way of our friendship.
Cocoa powder tempers that tendency and gives the dacquoise a slight bitterness that matches perfectly with the halvah.
He has a slight drawl that somehow sounds vaguely Texan.
With such a slight turnout, that did not happen.
