What is the punishment for a woman whose immodest photos were published online without her knowledge, and what should she do to seek her Lord's forgiveness?

It is forbidden to publish pictures of a woman who displays her adornments (mutabarrijah), or of a woman wearing a hijab if she lifts it. You have done well by requesting the deletion of the pictures. There is no sin upon you for the picture spreading by mistake, for Allah Almighty says: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts intended." There is no expiation upon you. What is obligatory is to be cautious about photography and to beware of non-mahram men seeing the pictures. Any act of obedience you perform is a good deed that draws you closer to Allah.