I've got a Canon S450-printer (which is somewhat older, I think) and Printer Status window in the menu has Option>Always Show Current Task (or even Option>Always Show) which, when checked, according to the Help set the window to always show while the printer is printing, exactly as you describe.
Could it be that your version has the same flexibility built in? Then simply uncheck this option.
When one of the cartridges thinks it's nearly empty this screen is showing much more than when they are all full, but it does obey to the minimize or close command or maybe (I can't check now) disappears after a few seconds spontaneously. Most of what I print is black, so especially if one of the colors is nearly empty this can go on for quite a few weeks.
Hope this helps.
How to get rid of it? Canon says to minimize it. But for me it pops up when the printing starts; I minimize or close it; but it pops right back up; I minimize or close it; not to be oudonw, when the printing is finsihed, it pops up again, though this time it has the common courtesy to disappear shortly.
I presume that other Canon printers have the same "feature". Maybe someone knows a way to get Canon to just do its job without advertising that it is doing so.
I had an HP printer which had a popup but it was there just a few seconds, whereas Canon likes to be sure you're interrupted for a considerably longer time.