UTC is maintained by a network of atomic clocks located around the world, which are highly accurate and stable. These clocks are not affected by local variations in gravity since they are designed to measure the fundamental properties of atoms, such as the vibrations of cesium or rubidium atoms.
While local variations in gravity do introduce small differences in the passage of time, these differences are typically negligible for most everyday purposes. For instance, the time dilation effects between different regions on Earth or within our solar system are incredibly small. However, they become more significant in extreme scenarios, such as near black holes or in cosmological contexts.
In summary, while gravity does affect the flow of time, we have established standards of time that are based on highly precise atomic clocks, which allow us to maintain a practical and consistent measure of time across the globe.