@the-muffin-top: Hi Gayatri,
Since you sought to add a search bar in the first place, it seems that you aren’t using my Disable Search plugin (which, as the name indicates, seeks to disable search entirely).
I’m not familiar with the Foodie Pro theme so I can’t advise too much on the specifics of how the search field is implemented. Have you tried asking for support from StudioPress?
This might help:
https://stackoverflow.com/questions/46363358/remove-search-form-from-menu-in-wordpress-genesis
Or this looks to be an improvement of the menu bar search field:
https://sridharkatakam.com/responsive-menu-with-inline-search-in-foodie-pro/
Based on that last link, though info is hidden behind a paywall, it starts off with how to disable the search form in the menu.
It says to change:
$menu_search = sprintf( '%s</li>', __( genesis_search_form() ) );
return $menu . $social . $menu_search;
I imagine the hidden next step (which should be all you need to simply remove the menu bar search field) should be to replace that with:
return $menu . $social;
If you want to implement the responsive menu bar search form (as shown in that video) which will allow it to show up on the mobile version, you’ll have to sign up for that site to get the code.
That’s about all I can do for you. No guarantees about any of the above. Hope that helps!