As it’s just the rear glass, and the impact doesn’t seem to have gone further than that, I’d get it fixed. There’s lots of places that can do it, Apple are making it easier for 3rd party repairs to be done, and as there’s no sensors involved it shouldn’t be too expensive. I think I’d get a more substantial case for it too – that’s quite a hard impact caused that!
My current phone has an Otterbox Defender on it, with a toughened glass camera lens protector and screen protector, but I’ve been using Ringke Fusion cases for some years and they’ve worked well – they have a lanyard fitting and I’ve used a lanyard with a snap buckle for years to attach it to my belt or a belt-loop, to avoid dropping the thing.
ampthill’s phone, though: #prayforampthillsphone