Great news! I found a way to change the completed date for tasks, if you also use TD with an Android phone (If you don't use Android and still want to be able to change the completed date then feel free to shoot me an email at firstname.lastname@example.org. I've been developing a separate utility program that can change the completed date. It's still under development, but if there's enough interest then I'll try to push through it faster). The "DGT GTD" android app allows you to change the completed date by going into the task detail screen > Menu > Task info. Also, if this is the only change that you're making, then some other detail (i.e. note, etc) needs to by modified in order for it to sync with TD.
It's a great app and the developer has been very responsive.