Great advice
Mike, what obligates you to say you can fix something based on a picture? Leaving aside whether or not your schedule will allow it, you have to stop right there and say:
"I can't tell you whether or not I can fix it without having the furniture available for thorough inspection and testing. Even with my ability to do both, stains of this nature on what appears to be a natural fiber are not always removable and I won't know until I try a few things, all of which will be charged for because they involve time, material, and my best people".
"In my attempts to correct this, the fabric may become whiter, may weaken and split, or experience texture distortion. I'll be asking you to sign off that you won't hold me responsible for any of this potential damage, though I will do all that I can to avoid that happening.
"If you have other alternatives, you might want to exercise those instead. Otherwise, I need $xxx.xx whether or not the outcome is successful."
I know those seem like hard words in an industry where we offer "satisfaction guarantees". The issue here is you cannot offer that type of guarantee on a delicate fabric that has been exposed to GKW ("God Knows What") can be damaged by the steps you'll take to attempt to fix it.
You'll ultimately need something with sodium percarbonate in the formula, which will begin to weaken the fabric. Strong direct applications of peroxide will surely weaken it worse, plus both may cause it to become more bleached in appearance.
Very little good will come from trying to do this without some strong guarantees from you customer that they will pay you and not hold you liable, and no guarantees from you, outside of the fact that you'll try to do your best to restore it without damaging it, but can guarantee neither.