What would you do with this covered deck on a rental?

[Sebastian Gast]

I am about to start turning a property rent ready and have a deck in the backyard (see pictures below).  I am trying to decide if I should keep it as-is or remove the roof.  A covered deck is nice in such a hot climate like Houston.  However, let's just say the roof looks like a civil engineer didn't design it.  

So... would you keep it? Or tear down the roof? I don't want it to turn into a liability but I could just be overreacting.