Time dilation is a misnomer. Time does not dilate; matter changes behavior when placed in distinct spatial positions.
When satellites are launched from Earth, they end up in a different spatial setting.
On Earth, matter is involved in four motions:
1. Big Bang motion
2. Milky Way rotation
3. Solar System swirl
4. Earth spinning
When the satellite is launched, the effect of motion #4 is reduced.
Obviously, the satellite will still be affected by motions #1, #2, and #3, and will have the after effects of motion #4, yet that simple move away from Earth, that is what is going on.
It is a bit like sitting in a train that has been going through an enormously long bend for quite a while. As passengers, we adjusted our position to get comfortable with the side-way pull (or push). But then, the train gets to a straighter stretch of track. The side-way pull becomes less. That particular motion relaxes while the train goes the same speed, and we adjust our own positions to this new situation.
That adjustment, that is what some call time dilation.
So, the wrong thing was appointed as the source. Instead of saying that the material of the clock adjusted itself (and showed a different time on its display therefore), folks said that time dilated.
That is like an old man joking that the tape measure stretched instead of admitting that he had shrunk a bit. The wrong thing got appointed.
'First Motion'