In order to reset your password in Tripwire, you'll need to log in using another method.

From the following screen, you can either click the blue 'Use API method instead' or click the EVE API tab above

This works since Tripwire stores your character rather than just an account.

From here you will be able to follow the 'View your API keys' link to go grab the original API you signed up with.

If that fails then pay attention to the circled text. Any API key you create should be limited to just Account Status permissions.

Once you have this key, go ahead and paste it into the keyID and vCode boxes and hit the login button. This will log you in as normal so you can change your password.

Changing password is done from the settings screen (cog in top right) as shown below:

You can then type in a new password:

Clicking save will set the new password and you're good to go!