but I do not know how to integrate that into the while loop for skipping the checks

I think you want

        ...
        if ( $columns[6] != 0 ) {

            # skip exclusions
            if (ref (my $excl = $exclusions{$columns[1]} ) eq "ARRAY")
+ {     # <---
                next if grep $_ == $columns[6], @$excl;               
+       # <---
            }
            
            $lastresult_of{ $columns[1] } = $columns[6];
        }
        ...
[download]

presuming you specify the exclusions as

$ ./941457.pl --exclude "robocopy dir"=3 --exclude "robocopy dir"=2  .
+..
[download]