Welcome to Android Central! I assume you have a Samsung phone. Picasa simply represents photos that have been backed up to your Google Photos in the cloud. When those backed up photos are displayed in your Samsung Gallery app, they have a little Picasa icon associated with them to signify that they're cloud photos. Those photos shouldn't be taking up significant space, since the actual photos are saved to the cloud -- the gallery app is only displaying the photos temporarily, unless you select the option to download them physically to the phone.
What do you mean it denies you access to the photos on your own device? Do you mean you can't seem to delete the photos using the Samsung Gallery app? If so, it's because those photos aren't actually on your phone -- they're in the cloud. The Gallery app usually can't delete photos in the cloud. You can use the Google Photos app, or go to photos.google.com on your computer browser and delete the photos there. But you probably have no need to.