I'm with you on this one, JoeCaption ---
I've bought and hung doors in two hours before, and I'm NOT some kind of semi-pro carpenter or handyman.
So long as the frame is reasonably square, a new door shouldn't take more than a couple of hours to install, and only costs about $180 for a cheaper steel exterior prehung door and frame.
My bet is you're going to spend way way more time trying to fumble around and fix that problem and make it look secure to a renter.
One thing I know about renting is that the quality of the renter you get is directly proportional to the rent you charge (not perfect, but usually true) -- low quality folks can't afford a high rent, and you won't get people willing to pay a higher rent if you hide a disaster behind some metal trim...
They have enough education/experience/common sense in life to see through things, or they wouldn't have the income they do.
(hedge fund managers and lawyers excepted here)
(side note - NEVER EVER rent to a lawyer... had a friend do that. He got threatened with six lawsuits from his renter in 18 months over crap the neighbors did that the landlord was supposed to have some control over??
Mainly, the lowlife was just hoping for free money settled out of court - no way the cases would have won in court, but it'd still have cost the my landlord friend plenty o $$$ to set foot in the courtroom and the lowlife ambulance chaser knew that, which is why the scum was after free money trying to get settlement out of court...)