Currently, deleting existing header in the Webhook connector doesn't work. At the same time you can update Webhook headers with the new header.

Steps to reproduce:

1. Create new Webhook connector in the Alerting and Actions page
2. Add a few headers and Save
3. Open created Webhook connector for Edit
4. Open Browser dev tool -> Network
5. Remove one of the existing headers and click Save
6. Find the PUT request which was sent for the current connector.
7. Check the response - it contains correct data for updated Webhook connector - header was removed.
8. Refresh the page and open the same Webhook connector.
9. Observe that removed header appears again.

Expected behavior:
Deleting Webhook headers should works.

Seems like some there is some caching issue on the server side for savedObjectClient.find