Does the emission of gas invalidate Umrah during Tawaf, and is it valid to restart it completely?

Purity is a condition for the validity of the Tawaf according to the majority of scholars, based on the hadith: "Circumambulation of the House is prayer." If one's Wudu' is nullified, they must renew it and then complete the Tawaf. If they do not, they must repeat the Tawaf if they are in Mecca; otherwise, they must slaughter a sheep. Some scholars, such as Ibn Taymiyyah and Ibn Uthaymeen, hold that purity is not a condition and that Tawaf is valid even with hadath (minor ritual impurity). Based on this, your 'Umrah is valid, Allah willing.