Why does a barometric pressure above 31.00 InHg trigger a TFR?
That is because most of the legacy altimeter setting barometers cannot handle such high pressures. Most of them, like the one pictured below has a range from 28 to 31 inches of mercury.
Kollsman Altimeter Setting Indicator, image from analogweather.com
7-2-4. High Barometric Pressure
a. Cold, dry air masses may produce barometric pressures in excess of 31.00 inches of Mercury, and many altimeters do not have an accurate means of being adjusted for settings of these levels.
As a result, the TFR is triggered by 14 CFR 91.144
(a) Special flight restrictions. When ... barometric pressure on the route of flight currently exceeds or will exceed 31 inches of mercury, no person may operate an aircraft or initiate a flight ...