I had same problem one time. I realized that on iOS, "X" doing action like Delete/Remove. Done or Cancel as exit action are better for two reasons:
1) a lot of iOS apps do so; iPhone user will be familiar with this solution; we are avoiding users confusion like on screen you attached
2) In my opinion, search field do not need great amount of space on mobile; I dont know any reasearch about that and destination of your app, but I think that users usually type first-ten signs from keyboard (in assumption that typing from mobile is usally less comfortable than other)
Keep it simple and consistent with platform, dude. :)