If you these values, then it may not be too difficult to get a good estimate of the exit gas water content. Use simple mass balance to get the exit water content in the gas, provided you have the following parameters also
a)Wet gas flow to the contactor, dry basis
b)Wet gas inlet water content
c)Lean TEG flowrate, dry basis
Careful with the wet gas water content, especially if you have high CO2 and or H2S at high pressures - see the GPSA for correction factors, or extract these from your process simulator with an appropriate EOS.