Is There a Way to Turn off the Notification Pop up That Takes up Like 1/4 of the Screen?

The 5.1 update is just not ready for your make/model of phone then. But that's the only real solution to your issue. Until then you're just have to either wait for the notification to disappear if you want it to stay or swipe it away. Hopefully the update will come out soon though, it's very handy to be able to swipe them up

As I said earlier, you can not swipe it away. And it will not disappear by itself. The Back button also does not help as it is handled by the app that you were actually using before the banner appeared. The only thing you can do is stop what you were doing and open the message.
Or completely disable the apps that do that - this what I would expect most people will do.