If she forgot to remove Face ID, then she forgot to erase the iPhone entirely. You won't be able to remove it without the passcode, and even so you'll run into other issues because she didn't properly erase and prepare the iPhone for you. If your wife is still logged into that iPhone with Find My, tell her to Erase then Remove the iPhone. If not, since the erase sign out process will require her Apple Account credentials, passcode, and other sensitive information of hers, you would want to send it back so she can erase it.
What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support