The Google Script will archive all email threads in a specific Gmail label that have been inactive for more than a week. It takes the date of the last message in a thread and if it is older than a week, the thread is archived. The current labels is removed as well.

function ArchiveOldEmails(gmailLabelName) {
  var gmailLabel = GmailApp.getUserLabelByName(gmailLabelName);

  var ONE_WEEK = 60 * 60 * 24 * 7 * 1000;

  var threads = label.getThreads();
  var now = new Date();

  for (var j = 0; j < threads.length; j++) {
    if (now - threads[j].getLastMessageDate() > ONE_WEEK) {
      threads[j].moveToArchive().removeLabel(gmailLabel);
    }
  }
}