Using this approach, your new file will contain a literal [fo]* as expected. Alternatively, you could use backslash escaping to tell bash that [, ] and * should be treated literally rather than as wildcards:

$ echo \[fo\]\* > /tmp/mynewfile.txt

Both approaches will work identically. Since we're talking about backslash expansion, now would be a good time to mention that in order to specify a literal \, you can either enclose it in single quotes as well, or type \\ instead (it will be expanded to \).