For those struggling to link an application to GC Key and running into an issue possibly due to 'city/town of birth' mismatch here are my two cents- I referred my COPR that has the place of birth. In my case, it was "City (UPPERCASE) [space] Two letters of state (Uppercase)" Example:
MUMBAI MS -> MUMBAI is city and MS stands Maharashtra (state). In no time system fetched my PR application but not the paper-based renewal one which was received this week by IRCC. Having said that, worth giving it a shot who knows this approach may work for most