All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
As we have previously highlighted in fataawa 85816 and 92400, according to the preponderant view of the Muslim scholars, that it is obligatory on the woman to cover her face before non-mahram (marriageable) men. Hence, it is impermissible for your wife to remove her niqaab just because people stare at her because of wearing it. If this is inconvenient for you, you can simply refrain from going to such restaurants. You can find other places where you can eat without facing such inconveniences.
We have previously underlined some guidelines relevant to women going to restaurants so, please, refer to fatwa 83500.
Allaah knows best.