You can clean it up a bit manually and save it as a bmp or png, but you can't just "unsave" the unwanted pixelation because it is now part of the image.

jpg is a lossy compression format,
the errors introduced are part of the jpg specification for high compression. As Ezzeral said use a non loss form

Hmm... I disagree with almostbob's assessment. He's right... JPEG is lossy, but that doesn't necessarily equate to the issue you're seeing.

Paint's JPEG implementation is crud. What I typically do when I want to take something from paint and turn it into a JPEG is first save it as a BMP from paint, then fire up Microsoft Office Picture Manager, and use that to turn the BMP into a JPEG. Picture Manager allows you to choose how high the JPEG quality should be. Crank it all the way to 100% and you'll see none of that extra junk you're talking about.

If you don't have Microsoft Office Picture Manager, don't worry. Download and install GIMP (Google "GIMP" all caps, it'll be at the top of the list). It'll do the same thing for you, and it's free.

Unfortunately, if you don't have a BMP copy (without the extra pixels) of the file, you're going to have to clean it up manually. You may want to play with the GIMP a bit and get to know it, as it is very powerful and might have some tools which could help you clean up the pixelated mess that Paint produces.

Good luck!

Yeah, i agree with PirateTux (if i remember rightly, JPEG support for paint was a hack they put in in order to get active desktop backgrounds working correctly in windows 98, it wasnt intended to have it originally...)