Niece invaded my iPod

If she activation locked it to her Apple ID it is essentially her iPod now.

Find My iPhone Activation Lock - This is a security feature, in part to deter re-selling of stolen devices.

http://support.apple.com/HT201365

Turn off Find My iPhone Activation Lock (formerly: Activation Lock: Removing a device from a previous owner’s account) - An activation lock can only be removed using the log-in information for the account that applied the lock.

https://support.apple.com/HT201441

Get her to remove it remotely in her iCloud using a browser: iCloud: Remove your device from Find My iPhone - http://support.apple.com/kb/PH2702

"If you’re no longer using an iOS device, an Apple Watch, AirPods, or a Mac, you can remove it from Find My iPhone using Find My iPhone on iCloud.com or your device. When you remove a device, it’s removed from your Find My iPhone Devices list, and if your device has iOS 7 or later, Activation Lock is also turned off."

Apple may remove a lock if a person can provide sufficient evidence of valid ownership. The device is normally taken to an Apple Store with identification and the original sales receipt. I.e., the receipt when the item was sold to the first owner, and preferably by that person. There is apparently no set policy (I asked at an Apple Store) and a store may simply refuse, particularly if they are not satisfied you have proven ownership by provenance.

When you say a factory reset won't undo it, I think that means there is an activation lock. That's the only personalization that would normally survive a factory reset. Unfortunately having your name on the phone might not be sufficient. You could have a stolen phone that has no passcode on it but had a the original ower's user ID in Find My settings. You could change everything but that to your ID, but it would still be a stolen phone. That's why having an original Apple receipt with your name and the serial number of the device on it is pretty much the only other reasonably convincing way to demonstrate it might be yours. Even then I can think of scenarios where that might not be reliable but that's up to Apple to decide.

Do you see a message saying tehre is an "activation lock", with her partial email address in it?