Corion mentioned placeholders, which is what you should be using here.

while ( my ($key, $value) = each(%uword) ) {

   my ( $owner, $om, $manager );

   my $select = qq/SELECT r.owner, r.om, r.manager /;
   my $from =  qq/FROM r, n /;
   my $where = qq/WHERE MATCH(r.owner, r.om, r.manager) AGAINST(? IN B
+OOLEAN MODE) /;
   my $likedate = qq/AND n.time LIKE ? /;
   my $join =     qq/AND r.key = n.key/;

   my $query = $select . $from . $where . $likedate . $join;

   print "SQL: $query\n";
   my $sth = $dbh->prepare( $query );
   $sth->execute( '+'.$key, $date.'%' );
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