Tenant Says They Had A Verbal Agreement With Prior Landlord

[Tariq B.]

Hello all, I took over a property last year and inherited tenants. The lease I have on file for them expires Oct 18 so we went month to month. It was a two year lease. I issued them a lease renewal with a rent increase. They are now saying they had a verbal contract with the prior landlord, who apparently said they had could have a 3 year lease (not sure why when it clearly states 24 months on the lease)

I know verbal contracts can be legally binding but what proof do I have? They could be lying for all I know. 

Would love to see what everyone has to add! Thanks 

-Tariq