Thanks Daniel.
The Linear Template I am attempting to remove is inside a Civil Cell. It seems it is not possible to remove the linear template in this condition - which is probably why I could not find the delete/remove button on the context sensitive pop-up menu.
I did track down the appropriate linear template from within the Project Explorer (and it took some finding!) and, from there, the delete option is available. When I selected that option, I get another message that says it cannot be removed because its in the Civil Cell.
Live and learn...