Hi Zach,
As a fellow Pixel owner, I've had and worked on the 2 XL, 4 and 6 Pro models, so I've been around them for a while now.
My advice would be to set your little metal cover aside somewhere safe and don't worry about it for now. Its only purpose is to secure the display connector so it can't get jarred loose, so your phone will work 100% correctly without it. The risk you run is that it's possible that one day down the road you may drop the phone or bang it against something and knock the plug loose. It's very unlikely but it could theoretically happen. If something like that were to occur and the screen goes black, then the first thing you'll want to do is open it up and make sure the plug is still in place. At that point you could put the cover back on.
The screen itself is very delicate and you run the risk of breaking it by trying to open it back up, so I wouldn't do it unless there was a compelling reason to. In my opinion, putting that cover back on isn't worth it.