1) The media library has 2 views-> 1 that shows all media items with thumbnails in a big list and one overview which has a table as an overview. You can switch between these two views by clicking the square buttons in the white bar on top of the page. Our plugin allows you to add columns for the table overview.
2) When you visit the table view in the Media Library and go to our settings page to manage the columns for the media table overview, it should not remove the default columns. I still figuring out why this happened on your environment, but I expect that you never visited the media table at all, which is the only use case in our plugin where I can imagine that it could happen.
3) The restore columns button stores the table overview to its default columns, the ones that the media library shows by default. In other words, our settings for the media library will be deleted and you will fall back to the WordPress defaults. In your case, the filesize column will be deleted and you will have back your default media library page.