Did you try calling and asking?
Finally there’s also Nexus. Nexus allows expedited entry into Canada in addition to full Global Entry and PreCheck privileges.
And get this, despite offering the most benefits of all 3 memberships, it only costs $50 every 5 years!
However for whatever reason, the credit cards don’t officially refund Nexus membership fees.
I originally enrolled in Nexus on my AMEX Platinum card. Of course it didn’t automatically credit the $50, however a chat agent was able to manually refund the $50 fee.
The main caveat of Nexus is that you must apply for it at the Canadian border. I had planned to apply in Detroit or Buffalo, but in the end I wasn’t able to make it up there. I wound up applying for Global Entry for myself, my wife, and our 2 kids as we were able to apply for it locally in Cleveland and those fees were automatically refunded.
It’s the best money I never spent.
https://www.dansdeals.com/credit-cards/ddfb-question-of-the-day-global-entry-or-tsa-precheck/