Firstly, get an exchange between you so that you have their admission by email.
With that confirmed, you can not reasonably be held liable. In practice, I would suggest you offer to arrange for the problem to be treated but that they will need to finance this. It makes sense if - having got, say, three quotes in to indicate ‘reasonableness,’ - you arrange things so that the tradesperson ultimately liaises directly with tenant, not least so that tradesperson is aware who will be paying and that this is agreed between them. There is less chance of animosity this way… usually… but keep your finger on the pulse in terms of ALL communications and ensure you are cc’d into any email exchanges between them; in writing is ALWAYS most prudent so encourage this from the tradesperson.
It is the fair thing for the tenant to concede to this cost implication.
It shouldn’t have happened in the first place. It was their fault (as qualified) not yours. This can’t be left and must be treated urgently for reasons expressed in another reply.
Cant believe they admitted it but…