What they are saying, I think, is that it was the old stud. I'm speaking to them again tomorrow so can check.
The threads have come apart, they showed it to me this morning, he was quick to point out that they did they tension to Audi standards
I think Audi standards are 20Nm plus 45 degrees (which is just weird) if I've guessed your model correctly.
Also, don't think your model's kits (tensioner) come with a replacement stud by default. When they come with a new stud (50p...), it's because the manufacturer is effectively admitting that they are known to fail on replacement. Don't think that is the case here so replacing the stud is a matter of discretion by the garage.
My friend's take is it is grey zone. Technically your garage has done nothing wrong (assuming correct tension which we will never know) BUT
- wiser practice on replacing the tensioner would have been to replace the stud. Or at least have given you the option (for 50p...).
- they were the last ones to touch it and it probably would not have failed (so soon, anyway) had it not been duressed by undoing and refitting
Friend would have suggested labour free repair i.e. you buy the parts and they fit free. But thinks they are unlikely to do so because labour costs for rebuild will be high. Maybe more than car is worth!! Kinda depends what value they see in you as a long term customer (or complainer!!!).
All in all, unfortunate but probably could have been avoided with a bit more (not legally mandatory) care.