Security door with lock guard
It's called a "Thumb Turn Cover", "Door Latch Guard", or "Cylinder Guard" and installs under your thumb turn mount plate, so it should be a DIY job.

It took me a very long time to pick out my security door for this reason, it's very hard to find one that blocks potential reach-around disarms for less than $600.  The most secure ones I saw all ensured that the openings within an arm length of the latch were all too small for someone to just stick an arm in. Similarly, the only built in cylinder guards I saw weren't really deep enough to prevent a reach around.

For me, the point of the security guard was so that my girlfriend could open the front door to talk to someone if needed, but not worry about them trying getting into the house.  As adding a cylinder guards would won't protect against this for a quick moving intruder you may want to consider a "Screen Door Grill"  or "Screen Door Pet Gill" installed on the interior side at lock height instead. They mount with screws, so you could DIY it.