I go into Settings / Advanced Settings / Signatures
Both "HTML Signature" and "Text Signature" fields are empty.
When I write an email the default is a marked "Singature" checkbox, which produces the signature from my first post. I can put anything I like in the HTML Signature or Text Signature fields but it doesn't change anything, I still get the default signature.
I've had Touchdown on this phone for at least 6 months.