How to tell if refurbished iPad mini 2 has new screen or battery?

If you purchased from Apple through their online refrub store, then it will have a new battery as that is a standard replacement part for all Apple refurbished devices - https://www.apple.com/us_smb_78313/shop/refurbished/about

Note too that only Apple sells Apple factory refurbished devices, and only online. They do not distribute their Refurbished devices to any other selllers. So anything you buy marked “refurbished” from Amazon, other sellers, a carrier, etc are not Apple refurbished products. This other sources are selling devices they contract with some company or partner to refurbish devices, and what constitutes “refurbishment” will vary wildly (and ofthen means nothing was done other than cleaning up the device). Those devices from anyone other than Apple also will not have an Apple warranty.

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But a refurbished iDevice will always have a different model ID number ( found in the Settings app, General, About ), that will always indicate an Apple refurbished iDevice.

The model ID number will be different from the normal, produced as new device standard model device ID number.