I would make certain that the label is at the top of the item box in the print composer.
Then I would make certain the label had an opaque background.
From what I see, the grid is linked to the map, but the labels stand alone, so you have some control over rendering order in that respect. If you had a map with an image, and it was at the top of the item list, I believe everything beneath the map would be hidden.
Okay, Based upon your comment, and my reply to your comment, I tried what I suggested.
I then set the desired parameters.
Then in the print composer, I created a grid with only a frame, and annotations.
It seemed to work.