Does passing wind during Tawaf invalidate Umrah, and is it obligatory to repeat the ablution despite the difficulty due to the crowding, and what should be done if the remaining rituals have been completed?

Purity is a condition for the validity of the Tawaf (circumambulation of the Kaaba) according to the majority of scholars. So, whoever breaks their wudu' (ablution) during Tawaf and does not re-perform it, their Tawaf is invalid, and they must repeat it as long as they are in Mecca. If they return to their home country, they do not repeat the Tawaf, but rather they must sacrifice a sheep and distribute it among the poor of the Haram (sacred precinct). Ahmad (ibn Hanbal) is of the opinion that purity is not a condition; so, whoever performs Tawaf while impure must repeat it in Mecca, but if they leave for their home country, it is compensated by a dam (sacrificial offering).