Is it permissible to request ice with halal drinks if it is served with a utensil or hand that has touched alcohol?

If an instrument or a hand that handled alcohol touches ice, any drink that subsequently touches that ice becomes impure (najis). A Muslim should request that the instrument be purified or use a pure instrument. However, if the instrument did not come into contact with alcohol, the ice does not become impure merely by being placed in alcohol without contact, and it is permissible to use it.