All Twitter account information is handled through www.twitter.com. TweetCaster does not have permission to view your password information. We just use your existing username and password.
If you need to reset or change your password, Twitter have a few options available - even in cases where you can't access the original email account you signed up with. You can find instructions here:
Once you change your password, you will be able to log out and log back in with the new password in TweetCaster, but we can't change it from within the app.