Grrok stores your Google Reader username+password on the phone. It transmits this information to Google in order to login. As you would expect, your actions (such as marking an item read) are transmitted to Google so that they can carry out your actions.
Google's use of information transmitted to them will (to the best of the author(s) knowledge) be used in accordance with their privacy policy (the author(s) of Grrok have no independent way verify Google's compliance with their policy).
No information is transmitted to the author(s) of the software or (to the best of the authors knowledge) to any third party (aside from Google).
Aside from your Google Reader username+password, no information is stored on your phone once the application has ended.
If this policy is not clear and you require further details, please email grrokprivacyPARIS@coralbark.net (removing the French city from the email address first).