I just got around to doing this, though it's been a problem for quite some time. Most of the advice on here only 'hides' the Picasa album from you, but does not delete the photos entirely, and that was simply not acceptable to me. Not sure about the rest of you, but I don't like the idea of my photos just sitting out somewhere where I have no control over them. Anyhow, one of the users way back on the first page actually shared the most useful piece on here, and that's how to get to the actual Picasa site and delete photos WITHOUT having to completely redo your email account and google login, thus forcing you to redo settings. Go to picasaweb.google.com/home and login using your google email. From there you can actually delete (or do other things with if this is something you'd like to keep) your photos. I will warn you, it is a giant pain because every time it sync'd (daily for me) it created a new album. This means that every time you added pictures you've got an album in Picasa waiting for you. This is an issue because to delete the album, you have to open the album. Took me about an hour to delete about 150 albums. You might find a better way, but I did not.
picasaweb.google.com/home ->Login with gmail (or google+)->Delete photos
Now this won't get rid of them from your phone unless you download the newest version of the ap (which I didn't want to do). To do that, you follow the advice that has been given. Go to your gallery, select your menu button (three vertical dots at the top left) and select settings from the drop down list. That opens up another screen. Click on the big 'g' followed by your gmail account name. That should take you to the screen where you can select what you want to auto sync. Deselect 'Sync Picasa Web albums'. Now you won't sync anymore. Now, go to your main phone settings (should look like a gear). Somewhere in there, there should be an 'applications manager' button. Choose that. The top tool bar scrolls-move that to 'ALL' and find Gallery (alphabetical order). Once that is open, you have options to 'FORCE STOP', 'CLEAR DATA', 'CLEAR CACHE', and 'CLEAR DEFAULTS'. Click 'CLEAR DATA' and then 'CLEAR CACHE'. This should get rid of the ghost photos as well as not show any that you left in Picasa but don't want to delete. This did not delete any of my other photos or my albums. Hope that helps.
GALLERY->MENU->SETTINGS->g(gmail)-> Uncheck Sync Picasa
PHONE SETTINGS->AP MANAGER->ALL->GALLERY->CLEAR DATA, CLEAR CACHE
picasaweb.google.com/home ->Login with gmail (or google+)->Delete photos
Now this won't get rid of them from your phone unless you download the newest version of the ap (which I didn't want to do). To do that, you follow the advice that has been given. Go to your gallery, select your menu button (three vertical dots at the top left) and select settings from the drop down list. That opens up another screen. Click on the big 'g' followed by your gmail account name. That should take you to the screen where you can select what you want to auto sync. Deselect 'Sync Picasa Web albums'. Now you won't sync anymore. Now, go to your main phone settings (should look like a gear). Somewhere in there, there should be an 'applications manager' button. Choose that. The top tool bar scrolls-move that to 'ALL' and find Gallery (alphabetical order). Once that is open, you have options to 'FORCE STOP', 'CLEAR DATA', 'CLEAR CACHE', and 'CLEAR DEFAULTS'. Click 'CLEAR DATA' and then 'CLEAR CACHE'. This should get rid of the ghost photos as well as not show any that you left in Picasa but don't want to delete. This did not delete any of my other photos or my albums. Hope that helps.
GALLERY->MENU->SETTINGS->g(gmail)-> Uncheck Sync Picasa
PHONE SETTINGS->AP MANAGER->ALL->GALLERY->CLEAR DATA, CLEAR CACHE
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