It cannot possibly be 'worn' as there are no moving parts to 'wear'. Even if you screwed it in and out a thousand times the oiled thread would be scarcely worn. If it is unserviceable, it is broken. A cack-handed mechanic must have broken it. ( Yet another good reason to do one's own oil changes!).
I think the garage is clearly trying to take you for a fool. Yes, you should insist they fix it at their expense. If they refuse, I would consider towing the car back home for an independent inspection (e.g.AA), and having it fixed by someone else and suing them via the small claims court for the cost (and the cost of a hire car) if they refuse to pay. Do let us know the outcome, please.
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