You can follow this outline to accomplish your goal:
Create a small form within your HTML, with its action property set to CompleteProfileDisplay.jsp, containing an input field named email, with a target of _blank, and a method of post.
Have your function set the value of the email input field of this form to the given email address and submit the form.
A popup window will open containing the same results as your original request, but the data (email address) will be submitted as a POST request without being visible in the URL.
Like this:
<!-- make sure this form isn't nested with another form in your page -->
<form action="CompleteProfileDisplay.jsp" target="_blank" method="post">
<input type="hidden" name="email" id="hiddenemail" />
</form>
<script>
function editRecord(email){
var e = document.getElementById('hiddenemail');
e.value = email;
e.form.submit();
}
</script>
(Your question does not show that you are customizing the popup window's appearance in any way, so I am not considering that in my answer.)