Praise be to Allaah.
It is not permitted to enter the bathroom with anything that has aayat from the Quraan on it, because this could lead to disrespect of the Word of Allaah, may He be glorified and exalted. Therefore, your wife should remove this necklace before entering the bathroom. Our advice is that women should not wear any jewellery with aayaat or duaas on it, because there are a number of reservations about this practice, of which wearing it when entering the bathroom is just one.
Sheikh Muhammed Salih Al-Munajjid