MTR Tenant Is Requesting to Terminate Our Lease Agreement...Can I Keep Their Deposit?

[AJ Satcher]

Hello all hoping to get some advice on this situation here, this is a first for me.

I signed a MTR tenant to a 3 month lease (Mar 30 - June 29). The lease was signed by both parties Mar 22nd. 

In the lease agreement, we have the following clauses:

a. "On execution of this lease, the tenant will pay the landlord a security deposit of $1,000"

b. "If the tenant requires early termination of the lease, rent and deposit are nonrefundable"

c. "The Term of the lease commences at noon on March 30 and ends noon June 29"

Said tenant only gave me $500 on March 22nd and asked if it was ok to give the remaining $500 by March 29th, in which I agreed via text was fine. On the 26th, the tenant said that they would have the remainder of the deposit by the 29th and also asked if they could change the move in date to April 12th, which I also said was fine.

Fast forward to today April 5th, the tenant is requesting to terminate the lease and requesting back her deposit. Mind you, she never sent the remainder of the deposit. 

Am I in my right to keep the tenant's deposit and move on?