Continuity mistake: The amount of dirt on the Doctor's face changes between the Bath House and the exterior filming.
Continuity mistake: When the Doctor enters the desert room in addition to his coat, he is wearing a brown waistcoat with a white shirt underneath. When the shot cuts away and the back to the Doctor, we see him take off his coat but he is no longer wearing the waistcoat. Later when he collects his coat after the acid bath scene and he starts to look through the wardrobe for a disguise he is mysteriously wearing the waistcoat again.
Answer: It was never destroyed on-screen; it was intact at the end of the TV movie, and destroyed by the start of the 2005 series. It was destroyed in the novel "The Ancestor Cell," but in a completely different manner to what happened in the series.
DaveJB