Landlord now wants more money, but early liquidation clause is plain

A couple of days ago, I moved out of my apartment. The early
liquidation clause states exactly as following:

"In the event it is necessary for the Tenant to terminate the Lease
before expiration of the Term, the damages caused would be uncertain
and incalculable at the time of entering into this agreement.
Therefore, the parties agree that Tenant shall pay the Landlord a
termination fee equivalent to the sum of two (2) months rent as
Liquidated damages, or ...."

goes on to list other things, but these other things do not matter as
the conjunction "or" is used.

On June 24th, I paid two months rent. They are now saying I owe them
another $1000. They say they are sending a "package" to explain it.
Actually, I haven't talked to them, but they called my parents while I
was at work.

This pisses me off greatly, and I plan on asking them to show me where
in their stupid lease they find I have not met my obligation.

.