There's a perforated steel plate in the CRT just behind the glass called a 'shadow mask'. It covers the entire area of the screen. It's function is to make sure that the red, green and blue electron beams (coming from the electron guns in the neck of the CRT) only hit the correct phosphors. For example a beam from the red gun will only hit red phosphors. The mask is very precisely placed in relation to the guns and screen in order to achieve this.
A good illustration here.
It's important that the mask is not magnetised, even in a minor way. If it is, an electron beam intended for red phosphors (from the red gun) might be diverted hit the wrong coloured phosphors. A strong external magnet held near the CRT will certainly magnetise the shadow mask and make this happen. Your son and his magnet will do it for instance

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The danger is that this could lead to mis-registration of colours even after the magnet has been taken away. So getting magnets near the screen should be discouraged really. Sorry, I know it's good fun but that's life

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There are some coils external to the CRT that demagnetise the shadow mask every time it is switched on from cold at the on/off switch (stand-by won't do). It has to be from cold because the coils are driven by a part called a 'thermistor'. This starts off cold and then warms up quickly when the power is switched on. It's during this short cycle that demagnetising (or degaussing) takes place. It won't happen again until the thermistor has cooled right down. This takes about 10 minutes.
About the colours staying wrong after the magnet has been taken away: Colours should return to normal after a degaussing cycle has happened. Sometimes though, the degaussing components may not be able to entirely demagnetise the shadow mask. Then the colours will not be correct (electron beams are diverted and hit the wrong colour phosphors). For instance, an overall white picture may have purple or green tinges in some areas of it. Two or three degaussing cycles will often clear this problem. This can be a lengthy business because of the time it takes for the thermistor to cool down.
Sometimes the thermistor goes wrong and won't do its job (not because of the magnet though). You have to call the repairer when this happens. A simple repair but most people don't get any fault mended these days.