To make the round trip “The WordPress Way” on the “front-end” (doesn’t work in the context of wp-admin), you need to use 3 WordPress functions:

• add_query_arg() – to create the URL with your new query variable (‘c’ in your example)
• the query_vars filter – to modify the list of public query variables that WordPress knows about (this only works on the front-end, because the WP Query is not used on the back end – wp-admin – so this will also not be available in admin-ajax)
• get_query_var() – to retrieve the value of your custom query variable passed in your URL.

Note: there’s no need to even touch the superglobals ($_GET) if you do it this way.

Example

On the page where you need to create the link / set the query variable:

if it’s a link back to this page, just adding the query variable

<a href="<?php echo esc_url( add_query_arg( 'c', $my_value_for_c ) )?>">

if it’s a link to some other page

<a href="<?php echo esc_url( add_query_arg( 'c', $my_value_for_c, site_url( '/some_other_page/' ) ) )?>">

In your functions.php, or some plugin file or custom class (front-end only):

function add_custom_query_var( $vars ){
  $vars[] = "c";
  return $vars;
}
add_filter( 'query_vars', 'add_custom_query_var' );

On the page / function where you wish to retrieve and work with the query var set in your URL:

$my_c = get_query_var( 'c' );

On the Back End (wp-admin)

On the back end we don’t ever run wp(), so the main WP Query does not get run. As a result, there are no query vars and the query_vars hook is not run.

In this case, you’ll need to revert to the more standard approach of examining your $_GET superglobal. The best way to do this is probably:

$my_c = filter_input( INPUT_GET, "c", FILTER_SANITIZE_STRING );

though in a pinch you could do the tried and true

$my_c = isset( $_GET['c'] ? $_GET['c'] : "";

or some variant thereof.