if ($word eq $checkWord) {
    $word = "<a href=\"$checkLink\">$word</a>";` <---
}
[download]

should be

if ($word eq $checkWord) {
    $word = "<a href-\"$checkLink\">$word</a>";
}
[download]

better yet

if ($word eq $checkWord) {
    $word = qq{<a href="$checkLink">$word</a>};
}
[download]

You also opened WORDLIST twice in your &check_links sub, 1 before you looped through @pieces and then you on each iteration of @pieces.

Also your perl -c complained about @pieces being global when i checked it against your mod.

-bn