What is the ruling on saying, "May Allah have mercy on them," when offering condolences for deceased non-Muslims?

It is not permissible to ask for Allah's mercy upon deceased disbelievers, whether they were Jews, Christians, or others, because Allah the Almighty says: "It is not for the Prophet and those who have believed to ask forgiveness for idolaters, even if they were relatives, after it has become clear to them that they are companions of Hellfire." (Quran 9:113). And because the Prophet, peace and blessings be upon him, said: "By the One in Whose Hand is my soul, no one from this nation, neither a Jew nor a Christian, hears of me, then dies without believing in that with which I was sent, but he will be among the companions of the Fire." This does not contradict the Prophet's good character and his kind treatment of the People of the Book. Praying for the guidance of disbelievers during their lifetime is permissible. As for the Prophet's standing for the funeral of a Jew, it was out of reverence for death, not for the deceased.