I say do it , like what other options does the customer have , its clean it or replace it . Let them know its not really suitable for cleaning but it should be an improvment . Manage their expectations . Im pretty sure they say just clean it . bear in mind all the advice given above , do a small piece to check for dye running etc . I would put some of your prespray gold mix in a spray can and brush it in gently with a soft nylon brush by hand , then extract it with a handtool , or upholstery tool if u have one or the wand if u want . Spend a bit of time cleaning the tassles and they should look brighter , Rub some oxidizer into them if you have time .
The rug might look a bit odd when its wet but it should look ok when its fully dry , about a week indoors
or not so long outside in the Italian summer . Charge a bit more because it so exotic and had to hand cleaned