Two problems

• You want the search string to be matched character for characters, but the match operator expects a regex pattern. You need to convert it to a regex pattern using quotemeta or \Q..\E.
• You check if the search string is contained in any string of the array. You seem to want to check if the search string is equal to any string of the array.

Solution:

grep /^\Q$search\E\z/i, @arr
[download]

or

$search = lc($search);
grep lc($_) eq $search, @arr;
[download]