Tenant bed bugs issue

Grateful for your views/advice please.

My tenants moved in at the end of May and paid 6 months rent in advance. They bought some furniture from the departing tenant, which was a private arrangement between both parties.

The tenants have been in touch about a couple of relatively minor things, so I have a line of communication with them. However last week they informed me they have bed bugs, and say they believe they were bitten on the first night, which they told me nothing about. They have paid for 3 exterminator visits, again without my knowledge, which they say has not resolved the issue - apparently the exterminator is saying the bugs may be burrowed under the floorboards.

The tenants are saying if after the 4th and final visit this week, the issue isn’t resolved, they want a full refund of all rent paid, deposit refund and cost of exterminator. My issue is, given they didn’t inform me until last week and have taken it upon themselves to bring in an exterminator with no consultation, it’s difficult to see where the bed bug issue has originated from. Certainly the most recent tenant, or any of my previous tenants, have ever complained of such an issue.

What do you think they should be entitled to if anything?

Thank you for reading.

Not sure what they are entitled to but think I would bring in my own pest control and get a report/opinion.

Have you been given a report from the pest controller they employed?

Did they move in their own bed? If there weren’t bugs before they could have bought them in. Don’t know how you would prove it.