How to edit a lookup page layout
The fields that are shown when you click a lookup icon can be very helpful so you're sure you're clicking on the right record. Here is how you can change the fields that are shown.
In setup, navigate to the Search Layouts link for the object that is where the records are. Even though you might have clicked the lookup icon on an opportunity, the layout you're changing is for the records that are being displayed. In this case, it's Contacts.
Note: If the object is a custom object, you can find it under the Create > Objects > Name of Object menu. The Search Layouts are in a section lower down on the custom object page.