Bedbugs, Tenant or Landlord's problem?

Hi reddit,

I'm a landlord renting a house to a section 8 tenant in California. The house was newly remodeled before being rented. The tenant has been in there for 6 months now and called me on Monday of last week complaining about bedbugs. I had pest control people go in and confirm that it is bedbugs. Heat treatment of bedbugs for the house will cost about 1800 dollars. I am sure that the tenants or tenant's guests brought in the bed bugs. Who should pay for the treatment? Even if I pay for it this time, can I add an addendum to the lease saying tenants are responsible for all future pest problems? Would that be legally binding? Thanks!

Edit: Thanks for all your responses guys. The other co-owner of the house thought 1800 for heat treatment was too expensive so she opted for chemical spray. It will cost about 500 dollars for 3 treatments. Since the infestation is early stage, this should eliminate the problem. We are adding an addendum to the lease that says Tenants are responsible for reporting and treating future pest problems.