Can I legally kill Canada geese without a hunting license if they are causing damage to my property?

Canada geese are protected under federal law, and a hunting license (with an appropriate federal waterfowl stamp) and open season are required to legally hunt them in Washington. Where lethal control of Canada geese is necessary outside of legal hunting seasons, the action should be carried out only after non-lethal control techniques have proven unsuccessful, and only under permits issued by the U.S. and Wildlife Service Fish. Currently the only agency permitted for lethal removal is the U.S. Department of Agriculture’s Wildlife Services.
For more information, see WDFW's "Living with Wildlife: Canada Geese" fact sheet.