Is it sufficient to place a ghutrah or something pure to prostrate on only when in doubt about the purity of the carpet or the place, or is it also necessary to stand on something pure?

One of the jurisprudential rules is that certainty is not removed by doubt. Therefore, no attention should be paid to a sudden doubt regarding the impurity of a carpet if its purity is certain, unless the presence of impurity becomes highly probable or certain, in which case it must be avoided. The purity of the place is a condition for the validity of prayer; it is not permissible to pray on something impure. If impurity is found, it must be removed or a barrier must be placed to prevent the impurity from affecting the worshipper.