how do I get rid of the recents/favorites icons on the top of my iPhone5s?

I realize that with the upgrade of the system, the iPhones now have the banner of favorites and recent contacts when you double press the home button on the phones. But this becomes a problem when dealing with (in) significant others who are jealous and can search through the top banner to see who the last people who contacted your phone (regardless if you were responding). Other than removing all texts and phone calls from the phone, (sometimes I need certain information) how can I remove these names which are showing up at the top of the screen? It's not like press and hold on an app which then gets you into the edit wiggly icons to move or delete, that seems only to all or text the person.

If this is going to remain as a permanent 'feature', then there needs to be a removal system to it.

PS: I'm really starting to get tired of iPhones when they are getting as big as the Note or HTC - if I wanted to walk around with something the size of a laptop, I might just as well go back to the "brick" - LOL!