The thing with which a person performs tayammum must be pure (ṭāhir); and based on obligatory precaution, it must also be commonly considered clean, meaning that it must not be tainted with anything that causes disgust.
If one does not have a pure thing with which tayammum can be validly performed, then performing prayers at that time is not obligatory for him; however, he must make up that prayer; and it is better that he also perform the prayer within its time except if the situation has reached the point whereby he must perform tayammum with a dusty carpet or similar thing.[1] If it is impure, the obligatory precaution is that he must perform tayammum with it, perform the prayer, and make up the prayer afterwards.