Keep track of which ones you've found in a hash.

# assume %matches is declared before the loops
...
   if ( /$searchstring/i &&
          ! exists($matches{$searchstring}) ) {
       push @stringsfound, $searchstring;
       $matches{$searchstring} = 1;
   }
...
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If you dont care about the order the strings were found, you could eliminate the array entirely by initializing the %matches hash with the strings as keys, and the values as false, and set them to true as you find the strings.
Then change my above logic a little.