Bedbugs- tenant brought them in, feels the landlord is financially liable for removal

[Kyle Kipka]

I was recently notified by my tenants that they have bedbugs in their unit and they've obtained 3 bids from exterminators for removal. In all 3 cases it was the opinion of the professional that infestation was related to recent travel and the tenants have been in the unit for 6 months. 

The unit was vacant for a month or so prior to their move-in and had been professionally cleaned. They also admitted that the bedbugs weren't there until recently and that they likely brought them in but they still feel that I should be financially responsible for removal costs (averaging about $2500). 

I declined and suggested they move forward with the bid they felt most comfortable with at their own expense but they then seemed to threaten legal action in a veiled manner citing their understanding of Minnesota state law which they feel puts the duty for pest removal on the landlord. This property is located in Minnesota. 

I do not have a specific pest clause in my lease but I struggle to see how someone bringing bedbugs into my property after 6 months without them, admitting that they likely brought them in and having a professional opinion stating as much would then require me as the landlord to be on the hook financially for removal? Do I need to be worried? Property is not located in St. Paul or Minneapolis proper so I don't think this city has specific regulations for that but I will confirm.