You need to tell the widget that the colour has changed. When you do $colour = 'red'; you are changing the value of the $colour variable but the widget doesn't know you have changed anything, it's not like -textvariable where any changes you make show up immediately. The -textvariable stuff does some funky magic so that it catches any updates you make to the variable. Very few other Tk parameters work like that as there is a memory and possibly performance cost associated with it.

You need to change

$mw->Label(-textvariable => \$rightwrong,
           -foreground => $colour)->pack(-side=> 'bottom');
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to

my $RWWidget = $mw->Label(-textvariable => \$rightwrong,
           -foreground => $colour)->pack(-side=> 'bottom');
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and then add something like

$RWWidget->configure(foreground => $colour);
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into your check() subroutine.