Remove query var on admin pages when ‘Save changes’ pressed

This might be useful: there is a filter called removable_query_args. You get an array of argument names to which you can append your own argument. Then WP will take care of removing all of the arguments in the list from the URL.

function add_removable_arg($args) {
    array_push($args, 'my-query-arg');
    return $args;
}

add_filter('removable_query_args', 'add_removable_arg');

Something like:

'...post.php?post=1&my-query-arg=10'

Will become:

'...post.php?post=1'