What is the ruling on Muslims eating in the mosque from food sent to them from ill-gotten gains, such as if the sender is a bank employee who deals in usury, knowing that they are unaware of the source of the money?

There is no obligation to inquire about the source of income of the food deliverer, for the fundamental principle regarding the wealth and food of Muslims is permissibility, unless it is definitively known that the food comes from an illicit earning; in which case, one should abstain from it.