or on the web: unlink

Update: I cleaned up and fixed the OP's code:

sub Check_request_file {
   my ($file_to_check) = @_;
   local *_;  # Protect caller's $_.
  
   open(local *FILE, '<', $file_to_check)
      or die("Unable to open SPROC file $file_to_check: $!\n");

   while (<FILE>) {
      if (/SPROC\sName\:(?!\s[rR]eception)/) {
         close(FILE);  # So we can delete it
         unlink($file_to_check)
           or die("Unable to delete SPROC file $file_to_check: $!\n");
         return;  # Optional, since <FILE> will
                  # return false for a closed file.
      }
   }
}
[download]

• You had two names ($flat_to_check and $file_to_check) for the same var.
• I switched rename to unlink.
• I changed exit to return.
• I fixed the regexp ([r|R] vs [rR]). See perlre.
• I closed the file before attempting to delete it. (Not necessary on all OSs, but required on some.)
• I used the safer 3 argument open.
• I limited the scope of FILE.
• I added error checking to the open.
• I improved the error message for deletion errors.
• I simplified the condition.
• I removed some useless quotes ("$file_to_check" vs $file_to_check).
• I removed the useless empty else clause.
• Update: I protected the caller's $_. while (my $line = <FILE>) would also have worked, if the regexp is matched against $line.