Those are usually photos that were synced to your device from your computer using iTunes. They can only be removed by syncing them off again. Either uncheck the entire folder (windows) or event (iPhoto on a Mac) that they belong to and sync again to remove all the photos from the folder/event. If you only want to delete some but not all of them, delete them from the folder/event on your computer and sync again and those photos will be removed.
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Does this cover your situation…
Basically photos synced via iTunes need to be removed via the iTunes syncing settings - not manually on the device.
Delete button for some photos in the moments tab is disabled