Ground conductors should not be run through the CT.
The CT is monitoring all three phase currents and trips the relay if the phase currents don't add up to near zero amps. Fault current returns to the source outside the CT so the three phases no longer add to zero and the relay trips.
If the ground conductor goes through the CT, the CT includes the fault current in the phase summation, sees zero current and doesn't trip.
BUT - with MV cables with grounded shields or 3/C cables with integral ground wires under the jacket, you have to be careful. If the shields or the ground wire goes through the CT on the way up to the phase leads' termination point, that ground wire or shield ground has to be brought back through the CT, in the opposite direction, to subtract out the fault current. If that is not done correctly, the ground fault will not work and there will be nuisance trips.