If its footage that was shot while he was working for them then yes,100% they can use it. In the same way WWE can include footage of Edge in a highlight reel now if they want. They own it.
It gets a bit murkier if it's CCTV footage as UK privacy and GDPR come into play as its not AEWs footage, was in a private venue and would be published without (I assume) at least one parties consent.
With all the legal back and forth that's happened up to this point, there is zero way Punk hasn't seen this footage already so I doubt it's a huge gotcha moment.
