GPS satellites don't compensate for relativistic effects (except for the huge offset built into their atomic clocks), but receivers certainly do. The satellite orbits are slightly elliptical which leads to varying gravitational time dilation. If this is not taken into account, positioning is off by around 10 m [1]. This is an effect from general relativity, so it might be left out in simple textbook explanations.

[1] https://gssc.esa.int/navipedia/index.php/Relativistic_Clock_...