The time period over which pair production-annhilation occurs might be a small part of the correction here, but from my quick reading of TFA, I think the key phrase is "This results in a small correction to the angular frequency of a photon and thus its velocity," where velocity is the key word. Velocity of course is a vector quantity, consisting of both a speed (c) and a direction. The key aspect here is the direction; when the pair recombines, the total energy of the system is slightly different as the positron-electron pair is affected by gravity and thus may pick up a small positive or negative acceleration from the gravitational potential they are traveling through. When they recombine this will be reflected in the new velocity (c d) of the resultant photon, which is not exactly the same as the photon prior to pair production.
At least thats what I got, but I'm the wrong kind of doctor to be an expert in this. Any PhD's wanna weigh in and correct me, please do!