At some point of setting up the phone, you missed the Sync Picasa or Instant Upload setting. The photos are on google server, and the phone is a mere mirror of those galleries, so you can't remove them from the phone, unless you remove them from Picasa and re-sync it to update. But if you don't want to do that, and your aim is to just clear it from gallery, this is what I would do:
First of all, turn the SYNC off for picasa. Go to Setting, Accounts, Google. Make sure the Picasa is unchecked.
Now go to Setting, Application Manager and look for Gallery. Open the gallery and Clear All Data.
You can reopen the gallery and wait for the phone to refresh, or simply restart the phone. You picasa albums should be gone by now.