Your unzipped image is now in PNG format.
It also has a black surround around the perforations as you know. I suppose this is intentional to 'highlight' the perforations.
I have inserted your image within a table cell and printed it out with no grey background, also printed in PDF format, again, no grey background showing.
I would try another printer if you can as a comparison print out.
If all is well in the other printer(s), it points to your printer/setting.