Time Dilation on the International Space Station

https://en.wikipedia.org/wiki/File:D..._dilation.pngT

Why don't you measure time dilation on the ISS ?
Physicists are claiming that clocks on the ISS would lose 24.6 us/day,
whereas clocks on the GPS are claimed to gain 37 us/day. Since the
clocks are in free fall in both cases this seems highly unlikely to me.

However the physicists claim that,due to the higher velocity and lower
altitude of the ISS, the direction of the time dilation would reverse.
If it is really true this would indeed be a spectacular demonstration
of the correctness of Einstein's Special and General Relativity, but
I don't believe it myself.