The web part in question is called AdvancedIncidentSearchWebpart. By default this web part isn't into the Web Part catalog, so it isn't visible when you try and add a web part to a page. Because of this removing & replacing the web part from a page isn't possible.
To load this web part into the portal so you can add it to pages take the following steps.
- Go to Admin\Portal\Web Parts Catalog.
- Click the Add WebPart Catalog icon
- In the Class Name drop down box scroll down to the bottom & choose AdvancedIncidentSearchWebPart.
- Modify the Friendly Name & Category if so desired
- Click Save.
You can now add this web part to portal pages.