Removing T-Handle Lock for Shed

Hi all,

New to the site and wanted to ask for your advice.

My wife and I have just bought a new home and the previous owner did not leave behind a key to the shed in the back yard. As such we are unable to lock it and feasibly anyone could just walk into our back yard, open the shed door and take anything out of there (which is why all my tools and garden hardware is in the garage right now!).

I believe that rather than paying a locksmith, it would be cheaper for me to remove the t-handle door lock myself and replace it. However, I am not sure of how to remove the existing lock. There are two (what look like) allen key screws in the front of the lock and another in the side of the cylinder cover. However all the allen keys I tried in these slots did not loosen/unscrew anything.

Now I'm not a DIY expert at all so maybe these slots are not for allen keys at all, but that's why I'm here hoping for some expert advice. Anything constructive would be greatly appreciated, thank you.

Removing T-Handle Lock for Shed