Wait until he sees the intake manifold.
The easy fix (and less popular) is the "EGR Mod", where you used the VAG-COM (aka VCDS) to dial down the PWM of the EGR to the threshold of triggering a CEL.
But, people like the "Race Pipe" that replaces the EGR valve completely. Had one, would never recommend it, since you're also eliminating the butterfly that chokes the engine upon shutdown, so it actually turns off, instead of the occasional runaway engine, plus triggers a CEL, so you need a tune that bypasses the EGR without the CEL.
That's interesting with the butterfly valve thing. When he had the valve cover off this TDI, the rocker shaft driven injectors had wires going to them. I just assumed with the ignition cut, the injectors wouldn't fire?
Watching that brought back all the feels but I hope he researched and didn't just throw the standard 5w30 the customer wanted in the crankcase.
As was mentioned, you have no idea how much there probably was. He was just poking the bear at that point. Do a quick image search on google for "TDI EGR valve". Warning, you may have nightmares. Dirty US fuel coupled with grandma driving didn't help them at all.
He probably did exactly as the customer wanted in terms of oil.
Doesn't seem like he dug further into that intake either.
He did put a new glove box door on her per customer's request though. It's funny the scope of work he's willing to do for people.