What is the ruling if a Mutamatti pilgrim realizes after finishing that he was in a state of impurity during one of the two Tawaafs (Umrah or Hajj), but the specific Tawaaf is unknown?

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The ruling defaults to the most severe possibility, which is that the impurity occurred during the Tawaaf of Umrah. Consequently, the Umrah is invalid, and the pilgrim remains unreleased from the state requiring shaving/cutting hair. This necessitates a penalty sacrifice (dam) for shaving/cutting hair. Furthermore, the Hajj is treated as having followed the invalid Umrah, making the pilgrim a Qarin (one performing Hajj and Umrah concurrently). The Tawaaf intended for Hajj suffices for both rituals. If the impurity were assumed to be during the Hajj Tawaaf, the pilgrim would still be required to repeat the Tawaaf and Sa'i, as the Sa'i followed an invalid Tawaaf in either scenario.