Try to add the following PHP code snippet to the child theme functions.php file to do this
add_filter( 'basel_header_configuration', 'basel_custom_header_configuration', 1, 1 );
function basel_custom_header_configuration() {
return array(
'container' => array(
'wrapp-header' => array(
'logo',
'main_nav',
'right-column' => array(
'wishlist',
'search',
'cart',
'mobile_icon',
)
)
),
'secondary-header' => array(
'container' => array(
'categories_menu',
'search_extended',
)
)
);
}
And this CSS snippet to the Custom CSS area for desktop devices
.right-column .search-button {
display: none;
}