To delete the call history on ZTE permanently and securely, you'll need a professional ZTE Call History Eraser - MobiKin Android Private Data Eraser.
You can rely on it to delete the call logs on HTC permanently and
securely without zero opportunity to recover, and you are allowed to
preview the files in categories and choose selectively the data you want
to erase before deleting.
Usually, you can do that directly from your ZTE phone. Just choose the phone call logs you want to delete, long press it. Choose the [delete] option. If you can't do that, maybe you can ask help from coolmuster android assistant. It will scan out all data including the phone call logs from computer. Then you can choose them to delete easily.