It's kinda hard to explain Paint by words alone, so I created a little picture.
The original pic is the one in the top left corner, and using the square cutout tool, I just took away the entire background. That's the easiest way of removing jpg compression (if you aren't going to use that exact background). Then, you may copy that text (with the frame) to any other background pic, by choosing the pink as your secondary colour - and make it transparent by clicking on the bottom copy selection in your toolbar. That was what I did with the random palm pic.
Of course if you want the best results you should go over the text and edit away all the compression dots inside it as well - using the colour extracter and the pencil. Which is a time-consuming thing to do, but not as difficult as it sounds.
That was what I did with the top-right picture with the word "kill". That's what would have to be done, if you wanted that exact background. Basically use a colour of grey/blue/pink/green that is in the nearby area, and pixel over the dots (especially around the lettering) and make a smooth background.