The short version is that Einstein's "special relativity" should actually account for this. It takes into account the satellites that track the GPS of things and thus keep the clocks at either end synchronized. It would be a tiny difference, but keep in mind that we were talking about a tiny difference to begin with. that difference would be about 32 nanoseconds, and since that same error would be at both ends, that makes for 64...almost exactly what the team observed.
That's impressive but it's not to say the problem is done and dusted. Peer review is an essential part of the scientific process and this argument must hold its own under scrutiny from the community at large and the CERN team in particular. If it stands up, this episode will be laden with irony. Far from breaking Einstein's theory of relatively, the faster-than-light measurement will turn out to be another confirmation of it.