I would ask them if as part of their diagnostics they checked the pan, as a VAG specialist i would like to think they would know of this easy solution so would have just told you that a clean was needed.
They should also do a test drive before telling you its fixed so that should determine if its fixed.
There are options available to you if it isn't fixed but let's trust the
garage that they have diagnosed and will fix the
problem first. I know some people dont want to trust garages but thanks to the Internet, social media and
review sites, it is ill advised for most businesses to do a bad job.