Does the Hadith indicate that the Hoor will look upon her believing husband in this worldly life and monitor his deeds?

The hadith (definition) you mentioned was deemed 'hasan (definition)' (good) by At-Tirmidhi and 'sahih (definition)' (authentic) by Al-Albani. It indicates that a woman who harms her husband in this world is cursed by his wife from among the Houris (maidens of Paradise), who says: "Do not harm him; may Allah fight you! For he is only a guest with you, and he is about to leave you for us." How the Houris come to know what happens to the husband in this world is part of the knowledge of the unseen. This might be through Allah informing them, just as we in this world know about the Houris and their descriptions through Allah's informing us in the Qur'an and Sunnah (definition).