Group views exposed taxonomy filter terms based on parent
You have to use an additional module to influence how the Exposed filter is displayed: Views Reference Filter. 

This module adds special new Filters to Views that rely on (existing) Entity reference Views Displays to filter the View. Basically, it's filtering one View Display with another View Display. 

In your case, you first have to:  


create an Entity reference Views Display that shows all the Countries, grouped by their Continents. It will be the Term type of View, not Content.  

You're designing here what your Exposed Filter will later look like. 
List Countries as Fields, 
then use Parent item Relationship to show Continent for each Country, 
Group the results by Continent (Parent) field in the Entity Reference list settings  

You will now see a list of Countries grouped by Continents. 
Save the View


With this ready you can:  


edit your "Note" Content view, 
add a new Filter Has taxonomy term that has (reference filter) in its name, expose it, and choose the Entity reference Display you created in previous steps above. 
Use Better exposed filters module to display the choices as Checkboxes


You will now have a working Exposed filter by Countries that will be grouped by Continents.