Buying Refurbished comes with risks and BackMarket is no better. BackMarket has a mix of variable quality sellers so check individual seller review before you order. The fact that they have some sellers with pretty poor reviews is worrisome but I guess that's the business model. Takes a lot of scrolling to find the seller reviews but it's there.
I purchased a phone listed as fully functional, and on arrival it wouldn't properly charge due to poor connection port for the charger. The connection felt wrong (didn't click in) and immediately triggered an error message saying the connection is poor. It would charge for a moment then stop and repeat.
The seller replaced the phone with some convincing, but the whole process left me without a device for an extended period of time, and left me highly skeptical that the replacement phone would last. I don't know what reasonable phone refurbisher can't identify a faulty charging port . As of this review, the replacement made it to 5 months which is great.
Would I recommend BackMarket? Sure, at the same level as Swappa, Amazon, Best Buy, decluttr or eBay for refurbished - only when you have time to be without a device for troubleshooting, and be sure to scrutinize individual seller reviews. Then cross your fingers.