The GR effects here is on the scale of 1e-15s, i.e. several orders of magnitude less than observed 6e-8s. 7 orders of magnitude is "negligible" as GP correctly stated.
>Actually gravitational time dilation on Earth's surface is on the order of 1e-9. But still negligible.
it is compare to zero gravitation far from Earth. The effect i'm talking about is integral of gravitational dilation change along the path of neutrinos. This path is a chord under Earth surface - the 350 km down to 10km depth and the next 350km bringing back to surface. The dilation change is about 1e-16 per meter of depth.
