What is the ruling on the presence of a bead wrapped in a piece of cloth with magical inscriptions on it in the wife's purse?

The bead might be an act of sorcery, and sorcery can be nullified by lawful means.

The questioner should advise his wife and clarify the prohibition of sorcery and dealing with sorcerers, and instill in her fear of Allah Almighty's punishment. If advice does not benefit, then there is no harm in separating from her.

The questioner should maintain the morning and evening remembrances (adhkar), recite the Quran, and recite Surahs Al-Ikhlas and Al-Mu'awwidhatayn (Al-Falaq and An-Nas) three times in the morning and evening. He should also be diligent in praying four rak'ahs at the beginning of the day, and repeat "Hasbiyallahu la ilaha illa Huwa 'alayhi tawakkaltu wa Huwa Rabbu al-'Arshi al-'Adheem" (Allah is sufficient for me; there is no god but Him. In Him I put my trust, and He is the Lord of the Mighty Throne) seven times in the morning and evening.

For "no caution can avert destiny, and supplication benefits against what has descended and what has not descended."