Photoshop already has a noise removal filter:
http://livedocs.adobe.com/en_US/Photoshop/10.0/help.html?content=WS22CE3EDE-EC58-40ee-9A34-4083DB365429.html
The only other filter I'm familiar with is Topaz DeJPEG, which costs about $30. You can search for "jpeg artifact removal" for possible alternatives. (The "compression squares" are called "artifacts" in tech lingo.)