Invalid Verification Code Customization?
There's not a native way I can see to do this.

Neither of these are clean workarounds, but assuming you're referring to Craft 3, you could either write a plugin that extended Craft's ErrorHandler class and overwrote the handleException class, inspected for that particular error messae and swapped it with one of your own. You'd need to tell Craft to use your ErrorHandler in craft/config/app.php.

Alternatively, you write a plugin that mimics Craft's UsersController's setPassword method doing your own custom logic and have the user related emails point to your plugin's controller instead of the native Craft one.