I thought you want to delete the "woi" feature when you click the button.
But it looks you don't want to delete specified feature.
In your logic, each time you click on map the Map1_MapClick will be fired and a new feature with same key "woi" will be added, that's why you met the same exception.
Please let me know your delete logic, what's your target here.
For example: you want to delete a feature in clicked point.
I want to know your delete scenario, so I can help you complete the logic here.