This usually happens when the mobile menu is not assigned correctly or when the theme falls back to displaying all published pages. I would first check Appearance → Menus and make sure your custom menu is assigned to the primary/mobile menu location used by Storefront.
You can also try temporarily disabling plugins to see if one of them is affecting the mobile navigation. Clearing any caching plugin and browser cache may help as well.
I had a similar issue on a site where only a few links should have been visible, but the mobile menu displayed every page, including an official page for the game that was not part of the selected menu. Reassigning the menu location fixed it.
If the problem continues, sharing a link to the site would make troubleshooting much easier.
