The phrase “to give short shrift to” means: To cut short; to make quick work of.
The literal sense appears in Shakespeare’s The Tragedy of King Richard III, Act IV, scene 4.
Lord Hastings has just been sentenced to execution by the Duke of Gloucester, shortly to be declared Richard III, and is interrupted in his reveries by Ratcliff, ordered to oversee the execution, who says: “Dispatch, my lord; the duke would be at dinner: Make a short shrift; he longs to see your head.”
That is, though a condemned criminal was permitted time for confession or shrift, urgency might require that he be allowed no more than a few minutes for his shriving.
Hence, thanks to the long list of crimes punishable by execution, this urgency was so common in the seventeenth century that “short shrift” became a synonym with “least possible delay.”