(First, don't keep pressing the 'Submit Follow Up' button. After you've done it once, go back and do a 'Reload' of the WEB page with your browser. This is explained on the TOP of the Forum's main page. Thanks.)
Anyway, when I removed ours, I used a flat-head pair of plyers. Traditional plyers and needled-nosed plyers are useless. Since my panels were, basically, cardboard, like you, I had to remove each staple by hand. I don't think any of them came out with the tile. Sorry, I have no tried and quick method for you you.
Best to ya.
PS: I bought the flat-head plyers (with a build-in wire cutter) at Sears. It's all black.