First, nothing is being "saved in your Gallery". Gallery isn't a location, it's an app, and you can't save pictures to an app, only to a storage location.
Second, Gallery shows all pictures on the phone, unless the name of the picture file stats with a dot (which means "hidden" in Linux, which is the OS that Android runs on), it's in a folder with a dot at the beginning of the name, or there's a file in the folder named .nomedia, which stops the search as soon as it's seen.
When you turn the phone on or restart it, Media Scan runs and finds all the media files - pictures, videos, music, podcasts - and builds a database of them - names, locations and types. Gallery just looks in there for pictures and videos and displays them. (Media Scan doesn't list hidden files, doesn't look in hidden folders and stops looking in a folder if there's a .nomedia file in it.)
As FreezerMoosh asked, if you made a screenshot of the homescreen, Media Scan will list it. (I don't know if you can make a screenshot of the lock screen - My phone is never locked at home.)