This problem with the GTR-200/20 has been previously reported. I’ve ferried a RV-14 with that radio on Guard and had the same problem - making it useless for monitoring (Comm #1 was a GTN-650). I’d need to have test stand data to verify but I’d guess that the radio’s receiver front end selectivity is not that great. I don’t have this radio in any of my builds so I have just this one data point.
The bandaid is to make the wire connection between the 650 and the GTR-200 (or GTR-20) that desensitizes the GTR receiver when transmitting on the GTN-650.
This does however eliminate the option of split comms (pilot communicating on one radio and the copilot on the other radio on a different frequency). Perhaps few builders consider this an issue.
Mehrdad - is this connection made on your install? If so, then there are other potential causes of your problem to chase down.
Carl