$('.remove-member').click(function () {
    var toRemove = $(this).parent().text().slice(0, -1);
    var members = $(this).parent().siblings('input[name=group-members]').val().split(' ');
    $(this).parent().remove();
    removeElement(members, toRemove);
    members = members.join(' ');
    $(this).parent().siblings('input[name=group-members]').val(members);
});
In the above, everything works until the last line (setting the value to the string contained in members).  Displaying the variable members in the console displays the expected string, signifying that $(this).parent().siblings('input[name=group-members]') is traversing the DOM correctly.  My HTML is below:
<form method='POST' action='action.php'>
    <input type='text' value='[ GROUP NAME GOES HERE ]' name='group_name' />
    <input type='text' name='add-member' />
    <div class='group_member'>name01<span class='remove-member'>x</span>
    </div>
    <div class='group_member'>name02<span class='remove-member'>x</span>
    </div>
    <div class='group_member'>name03<span class='remove-member'>x</span>
    </div>
    <div class='group_member'>name04<span class='remove-member'>x</span>
    </div>
    <input type='text' value='name01 name02 name03 name04' name='group-members' />
    <input type='Submit' value='Update' />
</form>
Directly referencing $('input[name=group-members]') is not an option due to the nature of the page.
removeElement function:
function removeElement(arr) {
    var what, a = arguments,
        L = a.length,
        ax;
    while (L > 1 && arr.length) {
        what = a[--L];
        while ((ax = arr.indexOf(what)) !== -1) {
            arr.splice(ax, 1);
        }
    }
    return arr;
}
 
    