What is the religious ruling on dealing with a wife who embezzled money from her work, and whose matter has been concealed, and she has pledged repentance and religious commitment?

You did well by concealing her fault and paying the amount. The Prophet, peace and blessings be upon him, said: "Whoever conceals [the fault of] a Muslim, Allah will conceal his fault on the Day of Resurrection." Her repentance should be accepted, along with addressing the reasons that led her to embezzlement. You have the right to reclaim the amount you paid if you did not intend to donate it, even if you paid it without her permission.