Either:

• Open the zip code (click it in the list, then the route row) and press the red DELETE button on the edit form; or
• Tick one or more rows in the list (or Select all zipcodes in <State>), then press Delete in the bulk-actions bar and confirm the prompt (Are you sure you want to delete N Zipcodes? for several rows, or Are you sure you want to delete 1 zip code? for one).

Deleting removes that zip + route combination only; the same zip on another route remains.