The purpose of the fuel damping relay is to control the low fuel light. It does this by monitoring the low fuel switch which is located on the fuel gauge in the fuel tank. Only when the low fuel switch has been operated for a set period of time does the module operate the low fuel light.
If you remove the fuel damping relay, then you should not get a low fuel light, but you should still have a fuel gauge.
So if with the fuel damping relay removed you still get a low fuel light, then it’s likely you have a wiring fault in the instrument wiring loom.