What is the ruling on greeting a working woman, and saying phrases to her such as "May God help you" or "Thank you," and does that contradict the denunciation by heart and tongue towards working women?

It is permissible to make supplications and express gratitude to a woman who has completed a transaction, as long as it does not involve jesting or laughter. This is based on the Prophet's (peace be upon him) sayings: "He who does not thank people does not thank Allah," and "Whoever has a favor done for him and says to the doer of the favor, 'May Allah reward you with good,' he has indeed praised him sufficiently." A woman's work is permissible if it adheres to Islamic guidelines, though her staying in her home is preferable. If she has committed Islamic transgressions, some female callers to Islam can be sought to advise her. Her transgressions do not prevent acknowledging her kindness and thanking her, as the Prophet (peace be upon him) used to acknowledge the good done to him by those who did it and loved to reward them.