Can I remove the default home button in ArcGIS online?
You won't be able to do this in the web map, but you can using the Web AppBuilder. You can choose to hide this widget.
Would you like to hide it in your web application using Web AppBuilder?
Home Button widget—Web AppBuilder for ArcGIS | ArcGIS
Hover the mouse over the Home Button widget and click the small eye icon to show or hide this widget in your application .
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