How do you continue a game app on a restored device that refuses to load the old game?

I have recently today restored my device since I have frogotten the orignal password to my iPod at that time. I reinstalled all of my apps, and most of them seems to load the old game I had on my device (thanks to my GameCenter account). But, there are 4 games that refuse to load the old game. Flutter: Butterfly Sanctuary, Mini Pets, My Talking Tom, and Naughty Kitties. The only game that mentions my game saved on my GameCenter account is Flutter, saying "Sorry, your Flutter account is already associated with a differnet GameCenter account." Flutter still plays from the start.

What I am trying to say is that there are games I redownloaded that will not connect to my GameCenter account after restoring my iPod. Is there any way to load my previous games back onto my restored device? The only app I really want to keep is Flutter, because I had made a lot of progress on it.

I'd recommend a person who's experienced with the apps I have listed to answer my question, but if anyone else knows a thing or two, go for it.