Is it permissible to withhold charity from a Christian cleaning lady after discovering her bad behavior and to seek out a deserving Muslim, or must one continue to give to her despite her previous behavior?

You are not required to return the charity to that Christian woman, because your charity to her is supererogatory, not obligatory. You have the choice to give charity to her or to a Muslim, and a Muslim has more right to kindness. It is preferable to allocate charity to the righteous and people of good, but it is permissible to give charity to a transgressor or a disbeliever. If you predominantly believe that your charity to her may be a cause for her embracing Islam or refraining from sin, then give her charity, and you will be rewarded, as in the story of the man who gave charity to a harlot, a thief, and a rich man, and Allah accepted it from him. All of this applies to voluntary charity. As for Zakat (definition), it is not to be given to a disbeliever.