The easiest way to clean your mystic topaz is to rinse it with a mild soap and warm water, and dry carefully with a soft cloth. Azotic, the creators of the mystic treatment, suggest using Windex.
According to Azotic:
The Azotic® Designer Enhanced Gemstone should not be exposed to any abrasives, acids, or immersed in an ultrasonic cleaner. Ultrasonic cleaners may contain a pickling solution that would cause damage to the Azotic® enhanced surface of the gemstone.
Abrasive cloths may scratch the Azotic® enhanced surface of the gemstone. This may not remove the treatment, but scratching the optical surface will affect the reflection of light traveling through the gemstone. This influences the color and clarity of the gemstone.
High heat may adversely affect the refractive index and eliminate color intensity. Heat should NOT be applied to the enhanced surface of the gemstone.