The internal degauss circuit is normally triggered either:
1. On command, by a button under the control flap, or via the control menu
2. Automatic, at power on (most televisions, and I thought older monitors).
The usual system has a thermistor to control the power, and needs 5 minutes rest to to reset to full power.
Depending on the severity, the discolouration may need 2-3 hits with the internal degauss (REST IT!) to clear. If it doesn't clear in 3 goes, it's probably beyond the capability of the internal.
If the magnet exposure was above a certain level, PERMANENT distortion of the shadow mask may have occurred - and that is why external degauss is a job for an expert, as the same kind of damage can be caused.