I also have a ModeS transponder (Trig TT21).
My "Own Transponder" issue was resolved with the update to the core FirmWare 3.31.
I know that this FW update particularly resolved the ModeS "Own Transponder" issue. I am not sure if it also addressed the ModeC "Own Transponder" issue.
(ModeS has the ICAO code encoded in the datastream which helps with recognition)