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.

Ensure that Sync Picasa Web Album is not checked. Click on the back button to exit as it will auto save.

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.

Click on clear data to clear the cache.
You should have successfully remove Picasa from your gallery.

Tested on Galaxy Note 4 Android Version 5.1.1