What is Terminal Annoyance?

The phrase comes from J.D. Robb's Conspiracy in Death, part of a mystery series set in New York City during the years 2058-59.  Eve Dallas, the series' protagonist, is a police detective who investigates homicides.  In Chapter 3, she visits a hospital to question a suspect:

Impatient, and because it was the section she knew best, Eve pulled her car into the ER lot, twisted it into a street-level space, then snarled at the meter that demanded to know the extent of the injuries she suffered.

This is an emergency only parking area.  Your injuries or illness must be verified in order for your vehicle to remain in this parking area. Please state the nature and extent of your injuries or illness and step forward to be scanned.

"I've got terminal annoyance," she shot back and shoved her badge into the view screen.  "Police business.  Deal with it."

While the meter squawked, she turned away to stride across the lot toward the hated glass double doors.