Is there any way to remove Ajax headers set by setRequestHeader()?

Is there any way to remove Ajax headers set by setRequestHeader()?

I'm writing a JS script that lives within a system which is now adding a
custom XID header to all Ajax requests via jqXHR.setRequestHeader() in a
function registered with jQuery.ajaxPrefilter().
In my script, I need to make an Ajax request to a third party site, whose
Access-Control-Allow-Headers is not set up to allow this custom XID
header.
It seems I have 3 options:
Find a way to remove that XID header in $.ajax()'s beforeSend function,
which I have confirmed gets called after the ajaxPrefilter() function.
Forgo using $.ajax() entirely and just write the Ajax stuff myself.
Have $.ajax() point to the system's backend which does accept the custom
XID header, and perform the request to the third party site via cURL.
Option #1 is preferred, if there's a simple way to do it, since it will be
the cleanest and fastest route. Just can't figure out how.
I have tried overriding it like this, but it didn't work:
beforeSend: function(jqXHR, settings) {
jqXHR.setRequestHeader('custom-xid-header', null);
}
Any ideas?