Thanks kindly for pointing this out. I use that control (in the de-selected mode) so that I can make to-do lists that I can read back later. I add a paragraph of text and then insert a checkbox in front of the text to build a home-made checklist.
But that is a little tedious, so I was hoping that there was a way to make completed Tasks more legible.
Sadly, the Strikethrough option shown above only applies to checklists, with no effect on Tasks inserted into Notes. But you are on the right track.