This is perplexing.
An Essure device is about 40-50 mm. That's only slightly longer than Mirena.

All I can imagine is that Essure has titanium in it, and it is coiled.

Above all, how can the so-called non-invasive AIT equipment see it?
Or is it not the AIT alarm at all? Perhaps the walk through metal detector is the issue. Coiled metal, albeit quite small?

If is the metal detector, I fail to see a work-around.
AIT equipment can have a software update to recognise an Essure.

It could make for some even more invasive passenger interviews for flights to the USA.
"Did you pack your bags yourself?"
"What is your boss' telephone number?"
"How much is your gym membership?"
"Which form of contraceptive technology suits you the best? Why?"
"May I see the serial number of your Essure device?"
"Which other forms of birth control have you tried? When? What did you like or dislike? Do you speak Afrikaans? Say something in Afrikaans."
"When was your last period? Was it 'heavy?' 'light?' 'inconceivable?" "Where did you eat dinner last night? What street was it on? What did you order?"
"Say your name."
"When was the last time you had chlamydia, and were you treated with doxycycline or azithromycin? May I see a printout of the lab results?"
And so on.