You can remove the Mailbutler badge from the Mail icon in the Dock.

1. Open Apple Mail and click on the Account Settings (⚙) button, then on Preferences.

2. In the new window that opens, click on the Account Settings button in the top right corner and then click on Show Mailbutler badge on Dock icon.

3. The Mailbutler badge will be removed from your Mail icon in the Dock.

To add the Mailbutler badge back to the Dock icon, simply follow the above steps again.