Does 'Umrah become invalidated by completing the circumambulation (Tawaf) and the rites after the occurrence of a minor ritual impurity during the Tawaf?

If you performed ablution (Wudu') after the impurity and completed the circumambulation (Tawaf (definition)), then your Tawaf is valid. However, if you completed the Tawaf after the impurity without performing ablution, then your Tawaf is invalid, because purification is a condition for it. In this case, you are required to slaughter a sheep in Mecca and distribute it among the poor of the Haram (definition), given your return to your country.