Sounds like they turned on Stolen Device Protection. Review this support article as being in a familiar location may help:
About Stolen Device Protection for iPhone - Apple Support
Did they also know your Passcode?
Did they know your Apple ID Password?
If they signed into your iPhone with their Apple ID, you will not be able to remove it without their password. Your only option then is to prove the device is yours by providing the original purchase receipt from Apple or Authorized Apple seller to have the Activation Lock removed. No receipt from any other third party will be accepted.
How to remove Activation Lock - Apple Support