Sure. Because there is no "real" form submitting going on here the input elements could just as well be buttons or anchors. You can remove all the form markup.
The jQuery (Javascript) listens to all click events on all elements that have the class approval (in this case its those input elements). When one is clicked, we extract the value attribute (Deny Contact Info[1,2,3,4]) and then call the window.open function with that value passed in the URL.
$(document).ready(function(){
$(".approval").click(function(){
v = $(this).attr("value");
url = 'deny_approval.php?section=' + v;
window.open(url, "myWindow",
"status = 1, toolbar = no, scrollbars = yes, location = no, resizable = no, height = 600, width = 600, resizable = 0" );
});
});