You can remove the start my day icon from the section: CPMInteractionPortalHeaderTopRight. After removing the start my day icon, I didn't notice any impact on the operator activities. Please find the below screen-shots for the same.
From CS 8.5 onwards all these rules were made as final. There are two ways to solve this issue.
1. The visibility condition: IsRoboticsEnabled which was there on the robotics icon should be false. This rule is final. But the condition it refers to here is the Declare_CAApplicationSettings.EnableRobotics = true. This property was set in the DT: CSExpressSettings which was there in the data-page:Declare_CAApplicationSettings. By default is was shipped to false. I think in your case, it was set to true. Make this to false so that this icon is not displayed in the interaction portal.
2. Another way is to customize the section: CSPortalHeaderWrapper to display your own icons.