have u tried changing ur wallpaper??? if the stain marks are still there on every wallpaper, yes there is water beneath it.
please share details on how u got the phone into such situation.
btw after reading some of the replies, u do not have a screen protector on a costly phone is kinda v questionable.
and the applecare doesnt really cover any water damage. so if the water beneath it damages any part internally, im afraid u would had to folk out a hefty price. however u are still able to use it despite the stain so i would say its not causing any problem.
if u do not have any more warranty, do not wish to folk out the hefty price, try going outdoor vendors like 3rd party ones aka ah beng store. but u risk getting carrot.
if u do not like that method then i would suggest going online to view vids and diy urself. screen replacement are pretty cheap and tools should be affordable.
vid guides are pretty clear and slow so u shouldn't have much problem.