Is our 'Umrah valid after my wife removed her hand coverings during Sa'i due to her ignorance of the ruling?

Wearing gloves during Ihram is among its prohibitions, necessitating a fidyah (expiation) but not invalidating the Hajj. The fidyah is either a sacrifice of a sheep or more, or feeding six needy persons, or fasting for three days. If your wife wore them out of ignorance or forgetfulness, there is a difference of opinion among scholars regarding the obligation of fidyah. The more cautious approach is to offer the expiation. If you choose not to, then you would be aligning with the madhhab of Imam Shafi'i and a group of scholars.