How to get rid of my deleted texts?

I have an iPhone 4 and when you slide your homepage to the left and search a word a bunch of my Really old texts come up tht had the word in it. Of course web I click on it the whole text doesn't show because it's delete but how can I get rid of them from popping up when I search a word? Some of them were deleted for a reason I don't want to see them again.

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