Hi Lauren! The reason you do not have that piece in the replacement part is because you are meant to use the one you currently have. I could not tell you for sure what the part does just from the picture, however it is important and appears to be connected to your main board. I don't believe it is a sticker but in fact a piece of hardware.
A lot of handheld devices use near paper thin circuits that literally "stick" on the phone backing or other surfaces. There appears to be writing on the piece, if you could post that or give us a clear picture of it, we may be able to use that to find out exactly what it is and does :)
If we take a look at the link below we can see the same piece very clear. Take a look:
The part in the picture above is a digitizer frame, and it does in fact come with the piece you mention. So I can only assume that the piece in your photo deals with your display and digitizer. It may even be the connection between your digitizer analyzing touch and that piece passing the info onto your motherboard.