They want to terminate the lease (month-to-month lease) and use security deposit as last month of the rent.Problem is there's no security deposit in the lease when I got this property from previous owner.

Is there a way to extract this from the security deposit and then have them update the security deposit at the time of new lease signing?

They could have done a "matching" program prior to taking the house into inventory, where a seller can indicate to zillow that they want to sell and they can find a buyer prior to taking ownership.- Optimize spreads between bid and ask: Zillow didn't do this. 

As such, I reimbursed the security deposit to them written to "The Estate of Tenant's Name".

After we agreed on a number, we moved forward with an agreement of sale form and deposit to the title company for escrow. 

Even i get a credit + rate match do you think 4.6% good rate with this credit

I would assume there is an early termiantion fee and the possibility of not receiving your deposit back, but you need to read the lease.

For the lower end (which matches my budget right now), his idea was a really nice, personalized luggage tag, which I think you can get for $25-40. 

They will send you paperwork to fill out to prove the ownership and enter in your direct deposit information for payment.

What does your contract say about deposits?