Does the whole rug need to be cleaned or is the homeowner just concerned with the water marking?
The water marking is questionable due to the contents in the contaminated water, amount overflowed, time on the fibers, and home remedies.
Regardless of the outcome, one needs to be reimbersed for ones time and effort. First attempt would be to post spray with an acidic solution. I have seen many use a solution of vinegar/water (hydroacetic acid) to remove the browning.
Keep your pressure low and do extra dry passes when cleaning. We will run something like Prochem All Fiber rinse through the system when extracting to remove the residue and prevent any future browning.
Good luck.