If I am understanding your situation correctly, the additional $200. is a higher security deposit for the unit you are currently renting.  If so, this would not be a "moving expense".  The security deposit is money that is deposited with the Landlord to secure your Lease and would be something that you are able to get back in the future.  It is an asset, not an expense, and it would be a profit to you if the initial Landlord would be required to pay your increased security deposit amount.  From what you posted, the initial Landlord was required to refund all of the money you paid to him/her already.

If you are confused about what "moving expenses" specifically means, clarify that in writing with the relocation department.  If the you and the clerk are not "on the same page", try politely asking for a supervisor to help clarify what exact moving expenses the initial Landlord is required to pay. For example, does "moving expenses" include a moving truck, for example, or just a total refund of all monies paid to the previous Landlord.

Let us know what you find out.  Good Luck!