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Do not remove the ASF (Anti-Shatter Film) just apply an extra scratch resistant film on top, the ASF it is not scratch resistant.
You could remove the ASF but i seems that it will void your screen's warranty, remember that gorilla glass it is not scratch proof but scratch resistant and it can crack, hence the ASF
If you remove the ASF you will need a new screen or at least a new digitizer if you want the ASF back, its not sold separately
I had applied matte finished scratch resistant guard when I purchased the Xperia SP. But due to one annoying air bubble, I removed it after a month. Since then (1.5 months) I'm using as it is. It seems to be okay. Not a single scratch on the screen. Just need to wipe finger prints frequently with a good cotton cloth.
I don't think scratch guard is really needed for Xperia SP as it comes with scratch resistant screen. I like to use phone as it is. But Its okay if you stick additional layer on it. Be careful with faulty/cheap scratch guards. They affect touch sensitivity also cause touch slip.