my $remove = quotemeta "{ (This Word) }";
print $remove; # See what happened.
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You can also shorten it to

my $text   = 'to { (This Word) }';
my $remove = '{ (This Word) }';

$text =~ s/\R//g;
$text =~ s/\Q$remove//; # <-- the \Q means quotemeta
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"What does the quotemeta do...?"

That's thoroughly explained in the docs. Ask your Teddy Bear ... uh, no, I mean, ask your machine's command line interface (using perldoc perlop [look for "Quote and Quote-like Operators"] or ask your browser using a search engine for http://perldoc.perl.org/functions/quotemeta.html which will tell you all about it.

We value sell-help self-help very highly here in the Monastery. You'll also find interesting (and helpful) information about site's expectations of those asking questions at PerlMonks FAQ section.

Edited: Typo fixed. TY soonix for catching what I should have.

Von_Halen: What does the quotemeta do in this case?

The quotemeta link says click me and read me