If you are just fitting the UEGO guage as a visual indication of the A/F ratio, you can leave both the white and blue wires disconnected. Make sure they cannot short to anything.
The blue wire of the AEM UEGO Gauge is for connection to a computer. You can capture and record the A/F values for analysis, adjustment, interest or just because you can. Probably not very useful unless you are adjusting / re-mapping the vehicles fueling. I have a connector on mine that I can connect to a lap-top.
The white wire is an analouge output that indicates the vehicles A/F ratio, in real time. The scaleing is be given in a table in the manual. This signal could be used for many things, including direct connection to an engine management system to provide closed loop control of the amount of fuel being delivered by the injectors. From the title of your post I assume this is what you are trying to do.
The AEM UEGO Gauge outputs both signals as a voltage measured between the signal wire and the black wire (0V, Chassis , Ground, or whatever you chose to call it)
From the information you have given on the greddy harness, it expects a A/F ratio signal that is differential. That is the A/F ratio signal is the voltage measured between the white wire and the grey wire. It does not measure it between a signal wire and ground. This type of system is generally used to eliminate noise that is present in the ground system.
It may be possible to connect the grey wire to the vehicle 0V, as close to the 0V of the gauge as you can get it, but I would not recommend it for something as sensitive as the fueling of your engine. Without knowing the full data on the what the greddy harness is connected to, I would say the two are not directly compatable. You will probably need advise from someone who has fitted one, or direct from the manufacturer.