I would apply a skim coat over top of what is there. Step 1: Clean away all loose cement and any other nastiness. Step 2: Cover your brand new patio with some plastic taped down in your work area so you don't mess it up. Step 3: Buy a flexible plastic trowel and cut it to the exact height you need to fit it into that space between the patio and the siding/doors. Step 4: Mix equal parts portland cement and fine sand, add water to make a paste and apply a thin layer over top of your nasty looking concrete to make it as smooth as possible. Step 5: Lightly wipe away any "oops" spots with a damp sponge (get the big yellow rounded edge sponges they sell in the tile section of big box stores). Best case scenario, you have a perfect looking concrete. Worst case scenario, you have a slightly better to equally terrible looking concrete. Good Luck!