How to quality check a refurbished iPhone?

If you are interested, we can probably tell you whether Apple refurbished the phone or another company did.....if you can provide the model number of your phone.

Settings > General > About > Model Number

If your iPhone is a Certified Refurbished iPhone purchased directly from Apple, here is what they have to say about their refurbishment process.

Why Refurbished - Apple

"You will receive a refurbished device with genuine Apple replacement parts (as needed) that has been thoroughly cleaned and inspected. Refurbished iOS devices will come with new battery and outer shell. Every device will come with all accessories, cables and operating systems. …

We back this quality commitment by including our standard one-year limited warranty with every Apple Certified Refurbished product."

If you got it from someone else, the "refurbishment" probably would not have been this thorough. Chances are you would not have a new battery, a new outer shell, or a one-year warranty.

No such service is offered. Did you purchase your refurbished device through Apple? That’s the only guarantee of genuine parts.

What does “full health check” mean to you?

This thread and

How much will a refurbished iPhone health… - Apple Community

seem to be by the same OP on the same subject.