I think you're not testing your code properly:
$ perl -wE '$_="\01\02"; say length; tr/\000-\007//; say length'
Nothing removed. (Update: But replaced, see Re^5: Illegal character CTRLCHAR code 27) Still you're on the right track. For deleting with tr///, you need a trailing /d:
$ perl -wE '$_="\01\02"; say length; tr/\000-\007//d; say length'
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