I had a similar situation few weeks back, mine was found during routine service inspection by BMW service technician. As per what they told me, since it is lodged on the outer side of tyre (and not towards the centre) it needs to be replaced and not repaired (or can't be repaired). They also cautioned me to change both tyres (in my case both rears) to reduce the risk of straining XDrive system (due to different tire tread depth and as a result different circumference. I ended up changing both...
after all tyre is much cheaper to replace than to deal with drivetrain related faults.