The World Federation One Stop Fiqh

Ruling 681

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.88 If it is impure, the obligatory precaution is that he must perform tayammum with it, perform the prayer, and  make up the prayer afterwards.

88 See Ruling 675.