On 9 April 2024, we updated the homepage and removed the other homepage layout options. This update removed the delete option. In a future release, we will reinstate the delete option, accessible via the menu button (three dots) at the end of the item row. However, the functionality will be different. You will only be able to delete the items you created or own. You can no longer delete (remove from your view) items that were shared with you.
In the meantime:
You can use the grid filters on the homepage to remove such items from your view.
Administrators can delete the favorites in your organization’s Phocas site via the Administration> Favorites page.