I would simply just charge the "rekey" to their deposit.  

Over the next 12 years I slowly mastered my HVAC, electrical, plumbing, carpentry, and locksmithing skills.

Give them 2 days to return it and if not, have the gate rekeyed. 

Or open a locksmith shop.

Like other said here, eliminate the handle lock or re-key the deadbold, throw away the handle key, is useless anyways.  

I will have to rekey the property.Is this normal being that it's a HUD home?

If the property is abandoned, and nobody has a key, you can ask for permission to hire a locksmith and change the lock. 

Each state has what they call "personal property disposal" laws.You need to check with your state to see what those are.Years ago when I did residential REO the asset manager would have me check the house to see if anyone was living there after foreclosure.If not the property preservation would come in and rekey the locks.Then they would want you to go in and see if more than 500 dollars worth of stuff was left.I would take the pics for the BPO and they would decide if it was over 500 value.If not they would order their company to trash out the place and not to eviction.If it appeared more than 500 was left even though vacant the attorney for the bank felt like they should do a formal eviction procedure to be protected from bogus claims by the former owner.This was in Georgia.You could call the power company and ask if your tenant has put in a change of service and turn off for the power at your unit or call the post office to see if a forwarding address has been given etc.

Bring a locksmith to the property.

Meet the locksmith and Do not go inside alone.