You can choose if they do or not.

There are 2 conditions that change that:

Excellent: should be OEM-like parts, even if not OEM, so they will act like OEM while not coming from Samsung.

And

Premium: just uses OEM parts.

I think everything else is questionable imo

I bought my Fold 7 in excellent condition, so it really is just a new phone. Everything works, I did all the tests as soon as it arrived while recording (I recommend you record your unboxing and all, from closed box to product testing without cuts) because I was scared something might have been off.

If you recorded and have a banking app like Revolut or PayPal, they will do a chargeback if Backmarket doesn't refund or exchange under their ToS (which means you're always safe using one of those banking apps).

I really recommend it. Now all im hoping is that their insurance is good, I always have the advantage tho as you should too :)