Where am I making a mistake?
You forgot to add a 500 ohm termination resistor across the load side. Doing this makes the net resistance seen after the 2475 ohm resistor into 275 ohms and this provides 20 db attenuation. Your source also needs to drive via 500 ohms.
I wish to design a balanced pi type attenuator to give attenuation of 20 dB and characteristic resistance of 500 ohms.
Also, your circuit isn't a balanced attenuator because you have one side earthed. Maybe you mean balanced in respect of both input and output being the same? Wiki quote from the above link: -
In telecommunications and professional audio, a balanced line or balanced signal pair is a transmission line consisting of two conductors of the same type, each of which have equal impedances along their lengths and equal impedances to ground and to other circuits.