I say, and with God's help: Purity is a condition for performing tayammum; because it is what is meant by "pure" in the verse: {So perform tayammum with clean earth} (An-Nisa 43). The place for tayammum must be pure, thus it is not permissible to perform tayammum on a place that had impurity, even if its trace has been removed without washing. As for prayer, it is permissible after the trace has been removed. And God knows best.