Honestly, EE would probably just remove it if you spoke to them and told them, depending how many months into the contract you are. They're really not the kind to take a hit for that kind of stuff publicly, and i'm sure they'd be more worried about you raising it to the ombudsman or something.
They also have a duty to not report false information to CRAs once they're aware of it - as far as I know. Ofcourse, that's the purpose of CIFAS, but I'd imagine they'd remove the account, can't say if they'd also add a marker