Click handlers that display the status of a submission
You can simply extract the common code into a function.  Arguably you could pass this rather than href and $target and derive ref and target in the function or pass $parent rather than $target, but the current arguments seem slightly clearer.  

$(function() {

    var fetchUrl = function (href, $target, color) {
      $(".spinner").show();

      $.get(href)
          .done(function() {

              var $parent = $target.parent();

              $parent.children("spinner").show();

              $parent.children("a").remove();
              $parent.children("span").remove();
              $parent.attr("class", "");
              $parent.css("background-color", color);

              $(".spinner").hide();
          });
    };

    $(".manualSubmitComplete")
        .click(function() {
            fetchUrl(this.href, $(this), "#B0FFB0")
            return false;
        });


    $(".manualSubmitReject")
        .click(function() {
          fetchUrl(this.href, $(this), "#FF0000")
          return false;
        });
});