vet:  Vet is short for veterinary surgeon. As a verb, it was originally used (in the 1890s) for ‘examine an animal medically’, but before the end of the 19th century this had broadened out to ‘investigate, screen’. Veterinary  itself came from Latin veterīnārius, a derivative of veterīnus ‘of cattle and similar domestic animals’.
"to submit (an animal) to veterinary care," 1891, from veterinarian. The colloquial sense of "subject (something) to careful examination" (as of an animal by a veterinarian, especially of a horse before a race) is attested by 1901. Related: Vetted; vetting.