Normally this does not happen. Are you sure the unwanted invisible characters aren't already in your text field?
You could try 'Select all' , 'Copy' an then paste in BBEdit (or another text editor which can show invisibles).
It turns out that FileMaker creates text files with 2 bytes per character, when exporting a field, whereas TextEdit only uses 1 byte per character (UTF-16, vs. UTF-8). Is it possible to change a setting in FileMaker to avoid this problem?