The noun “vet” originated became an abbreviation for “veterinarian”. By 1850 in Great Britain and Ireland, horse doctors were commonly called “vets”. By 1875, “vet” became a verb at the racetrack as in “the racehorse had only to be ‘vetted’”.
The “vetting” of horse progressed to was applied to people, a humorous way to describe a medical exam. By the early 1900’s, the British military began using the phrase to indicate that something had been processed or checked over. Within a few years, British politics began using “vetting” to describe a thorough check of a candidate’s background.
The verb was rarely used in America until 1980 when it began appearing in news reports about the Reagan administration, as in “candidates are being vetted for presidential appointments.” Now ensconced in US political jargon “extreme vetting” figuratively means “to subject a person or thing to scrutiny; to examine for flaws.”