The clause means whatever the Judge says it means. You should have taken the tenant's offer. Because, you face a very real probably of not getting anything. Did you get the tenants to initial this added clause? A hand written clause added to the lease without any tenant acknowledgement may be interpreted as a clause that was not properly discussed or explained at the signing or maybe added later. The Judge has to think about all of this. Lastly, the fact that you have already taken payment as settlement may mean the Judge will not reopen the agreement because you now have a different interpretation. Have your checkbook ready.
I didn't accept it. They just sent me an extra month's rent in their last rent check and I accepted it as partial payment of their breaklease fee. I never accepted their offer. I didn't get the tenant's to initial the clause. They signed it, but it was not discussed until they informed me they were breaking the lease and gave me their interpretation that the 2 months notice would fulfill the early lease termination clause in the lease.