As far as I know you get rid of it, only reduce what is shown there down to I believe 5 things. The only reason the screen should come up is if you swipe down on the screen.
If neither is the case, try first restarting the phone. Should that not resolve it, I would check the device for viruses, malware, bad apps, etc., to make sure nothing is causing it to react. If the device is clear, then try removing any apps that have been added to the quick settings. Not from the whole phone, just from the device settings screen. One that is in there could cause it to constantly come up.