Rather than calling the person who presumably rented the unit to them, they instead called a lock smith to change the locks!!

You won't need movers for the county just a locksmith which you can be along with ofcourse the locks. 

These locks can be easily rekeyed by yourself.

Systems include HVAC, plumbing, electrical, roof, foundation, windows, etc.Health and Safety - RequiredIt is important to provide a safe environment, which includes items such as smoke detectors, transition strips, trip hazard removal, lock rekeying, and more to ensure a safe environment.Items Necessary to Attract Your Target Tenant Segment - RequiredIf you want to attract a specific tenant segment to occupy your property, it has to match their housing requirements.

.- On the local regs topic those are the ONLY things you can collect except for a re-key fee (I've never done that and don't know anyone that does so it isn't customary and have no idea how much you can charge above cost and not get hauled into court).

It's all relative...You can also try larger locksmiths, and ISTM I once ordered a set through Home Depot or Lowes.

I tell my tenants that I'm out of town so they need to call locksmith. 

These are easy to rekey but they are still mechanical locks.

Landlord may deduct reasonable charges from the security deposit for: Damages to the Property, excluding normal wear and tear, and all reasonable costs associated to repair the Property; Costs for which Tenant is responsible to clean, deodorize, exterminate, and maintain the Property; Unpaid rent; unpaid late charges; Unpaid utilities and utility expenses Landlord incurs to maintain utilities to the Property as required by this Lease; Unpaid pet charges; Replacing unreturned keys, garage door openers, security devices, or other components; The removal of unauthorized locks or fixtures installed by Tenant; Landlord’s cost to access the Property if made inaccessible by Tenant; Missing or burned-out light bulbs and fluorescent tubes (at the same location and of the same type and quality that are in the Property on the Commencement Date); Packing, removing, and storing abandoned property; removing abandoned or illegally parked vehicles; Costs of reletting , if Tenant is in default; Attorney’s fees, costs of court, costs of service, and other reasonable costs incurred in any legal proceeding against Tenant; Mailing costs associated with sending notices to Tenant for any violations of this lease;Texas Residential Lease Agreement Any other unpaid charges or fees or other items for which Tenant is responsible under this lease; Cost to restore walls, flooring, landscaping or any alteration to the Property not approved in writing by Landlord; Damages to the Property caused by smoking, including but not limited to stains, burns, odors, and removal of debris; and costs to rekey certain security devices, as provided in Paragraph 19.2.

Regarding door locks I recommend that you change them or have them rekeyed during each turnover.