You can override post permalink via this filter hook.

you can add url parameter like this

add_filter('post_grid_item_post_permalink', 'post_grid_item_post_permalink_custom');

function post_grid_item_post_permalink_custom($link){

    return $link. '?arg=hello';
}

you can also replace url via the custom/external link

add_filter('post_grid_item_post_permalink', 'post_grid_item_post_permalink_custom');

function post_grid_item_post_permalink_custom($link){

    return 'http://hello.com/custom-url';
}