Because it is not well documented in the AWS docs herein is how you delete an AWS API Gateway resource.
- Click on the end point in the left hand side.

- Click the
actionbutton in the top middle, just right of the resource list. - Click the
deleteoption. - Enter the name of the resource and click
delete.
Wait 20 – 30 seconds and reload the page. You should no longer see the API resource listed.