Why did my landlord only give back a part of my security deposit?

You’re right; the landlord does need to do more. The landlord may keep part or all of a security deposit for certain narrow or specific reasons: to pay for necessary repairs or replace damaged appliances or furniture (if the apartment had either or both); to make up any unpaid rent; or to pay for cleaning beyond the normal wear-and-tear, such as if you spilled motor oil on the carpet, or kept a pet that had accidents in the apartment. (Note: a landlord specifically may not use the security deposit for pay for normal, end-of-the-lease, new-tenant-moving-in cleaning.)

However, the deposit is your money, and the landlord has to prove that she is entitled to any amounts that she took out. That means she needs to itemize any deductions for you, and typically provide the back-up (e.g. receipts) as well. This has to be done in writing, and is typically done in what’s called a security deposit settlement letter. Itemizing the costs and deductions is not optional; it’s mandatory and if the landlord hasn’t done it already, you can demand it.

Note that depending on the size of the building (the number of units, that is), the landlord may have had to keep the deposit in an interest-bearing account, in which case you’re entitled to the interest and the settlement letter needs to annotate it as well.