You can tell if your monitor does this by listening when it is turned on. If the monitor is warm, you can see the screen image warble as the degaussing is performed. If your monitor automatically degausses, then after removing the source of magnetic contamination, you may not need to do anything to remove the colored spot. After turning the monitor on and off many times through normal use, the spot should disappear. This should take a week or two.
Some monitors have a manual degaussing button.
Try pressing this button occasionally to remove the color problem. Do not degauss the monitor many times in rapid succession, as this may cause damage to the degaussing circuit on some CRTs. You may want to use a manual degausser, which is an electromagnetic device you wave over the surface of the CRT to remove the magnetic field. These devices can be purchased or rented but should not be necessary with most modern CRTs. If you use a manual degausser, be very careful to keep it far away from magnetic media, which it can destroy very easily.