Is it permissible for my wife to bathe with water that people have washed their hands in, with the intention of seeking healing from the evil eye, without their knowledge or permission, and is this act mentioned in the Sunnah?

The Sunnah does not indicate that washing only the hands is sufficient in treating the evil eye. Rather, what is established in it is the washing of multiple body parts, such as washing the face, hands, elbows, knees, ends of the feet, and the inside of the lower garment. Then, this water is poured over the person afflicted by the evil eye. The permission of the envier (the one who cast the evil eye) or knowing who they are is not a prerequisite for the treatment.