Picasa photos are automatically synchronised to your Android Gallery by default. I am going to show you how to remove Picasa totally from your gallery.
Goto Settings -> Accounts -> Google
Click on your email to access your account.
You will need to clear the gallery cache to remove the Picasa.
Goto Settings -> Application Manager
Slide the tab to All and find gallery and click on it to enter.
Tested on Galaxy Note 4 Android Version 5.1.1