perl -epi ...

Er, no. That executes the code 'pi' with the rest of the line as @ARGV, which is effectively a noop. Also there mustn't be a space between -i and its arg. Lastly, using \r is to be much preferred than a literal carriage-return control character. You want this instead:

perl -pi'.bak' -e 's/\r//' <FILE_NAME>
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Dave.