بسم الله الرحمن الرحيم
It is difficult to avoid the mud which emerges in roads after rain and it smears on back of the cloth while walking; therefore, it is exempted provided it does not have any visible impurity. You may offer your salah in the same cloth. And if the impurity appears but it is in such a quantity that is exempted yet salah will be valid in the same cloth; however, if one is sure then he should wash it. But if the impurity is more than the quantity that is not exempted then it is mandatory to wash it, as salah will not be valid without washing it.
طين الشوارع عفو . والعفو مقيد بما إذا لم يظهر فيه أثر النجاسة الخ . (شامى)
Allah knows Best!
Darul Uloom Deoband