You surely don't have to copy and paste, since the fields are already used by GSX, and they are pre-filled with data in the scenery AFCAD and are used by GSX even if you don't explicitly set them.
And, they are not directly GSX airline operators, but only codes in the AFCAD that GSX will use in weighing its choice of its own operators, when there's a tie in matching the airport ICAO.
For example, if you are at KLAX, which matches with the maximum score of 4 ICAO letters the following operators:
American Airlines ( AA in GSX )
Alliance Ground
ASA
Delta ( DL in GSX )
Frontier ( FFT in GSX )
United ( UA in GSX )
Southwest ( WN in GSX )
It means that, if the parking had NO parking codes at all, all those 7 operators would have an equal random chance to appear on a KLAX parking that had no codes, or no codes that matches these ones.
If, instead, the parking had these codes
AAL, AALX, UAL,UALX, LHA, TCX
Only American Airlines and United would have an equal random chance between them two to appear on that parking. LHA and TCX won't be used, because they didn't match the airport so, the codes are used to breaking ties amongst operators allowed in an airport.
If you look at the SIM.CFG file of any GSX ground vehicle (the Baggage loader for example), you might have a better idea how codes are matched.
Note that, if you *override* the codes (that's what you did by "copying and pasting" the codes), GSX will then IGNORE its internal airport restriction, allowing to choose any operator everywhere. That's why you probably thought you HAD to override the codes: because you were expecting these codes would always appear, but they don't: they are only used to break up ties amongst operators that matched the airport ICAO.
The reason why we don't use the AFCAD codes directly, but only for breaking ties, is because on an airport with international terminals, you'll see many different overseas companies, because they use that gate, but it would have been wrong to just allow them as ground operators, because you surely cannot find, for example, a British ground crew at KLAX *just* because British uses a gate at KLAX international terminal.
So, first an operator must match the airport, and then we look at the airline codes to restrict the choice so, for example, UA will appear by preference on gates with UA codes.
But of course, when you do an override, what you put there will appear, regardless of the airport so, if you want to have an Alitalia crew servicing the airplane in China, you can do that.