The issue of purity during ṭawāf differentiates the essential circumambulation from its requisite state of purity. In the Hanafi analysis, the core act may occur while performing it without ablution or in major ritual impurity produces deficiency and a compensatory ruling.
Depending on the kind of deficiency, repeating the act or offering a sacrifice becomes relevant. It is inadequate to compress every case into one unqualified verdict of valid or invalid.
Comparison: Purity in prayer and purity in ṭawāf do not occupy identical legal positions in this discussion. The difference concerns the underlying act and its required attributes.