Any metal you attach or screw into that lumber MUST be either stainless steel, 1st preferred choice, or hot dipped galvanized, otherwise the pressure treated wood will eat it like chocolate. There are books and plans on how to properly build things like Pergolas at H. Depot and on the net. You don't want that structure to come down, ever. Make sure it is properly attached at the house ledger.
How is it attached, the ledger board, currently?
It's hard to tell from your pictures. Take some more, showing and detailing what the fasteners are and where and how many there are.
You may want to consider some shade sail cloth material to cut down on the amount of sun that enters the area. It will make it cooler and can be retracted as needed if installed with that intent.
Post back more details.:thumbsup:
Update: on further examination, looking at the second pic you posted it looks like they used Timberlock black hex headed screws to lock the ledger board to the house wall, hopefully sized adequately and speced properly so as to attach to the exterior wall studs in every case.
What I don't like about the corner bracket attaching the ledger board to the end joist is the use of the yellow colored coated screws. Those brackets, and the hurricane straps, ALL need to be fastened with Tico nails, which are specifically designed for the application. Screws do not, with the exception of the Timberlock type, have the shear strength required to hold the structure from tearing apart in high wind/etc.
It's a simple fix, remove the screws and use a palm nailer to install the correct size Tico nails.
Again, you want to protect yourself and family/friends from catastrophic failure, which can easily be prevented, by doing thing right the first time.
Sorry to be the bearer of bad news, but anything of that amount of mass overhead must be properly fastened. Screws in the ties are NOT the way to do it.