As of now, the imported pdf is shown 'as is' without the option of adding background.

What would be convenient for pdf annotation is the option of showing a virtual grid (or other background) over the pdf contents; it will allow for much nicer handwritten notes.

When the annotation is done, the exported pdf does not have to include the grid (or whatever the background was). In fact, it would be very useful, if the exported pdf did not have the virtual grid (or background) at all.