Thunderbird is very specific about adding a double hyphen “–” signature separator to email signatures to delineate what’s signature and what’s just a template.
Technically, this just hides it, but if that’s sufficient, it’s fast and easy to accomplish.
1. Open a new message. Select the top two lines of the signature, including the “–” separator and the empty line above it. Copy them to the clipboard (Ctrl-C).
2. Just above the signature window, enable HTML (Use HTML).
3. Insert an html tag to turn the text white: <font face=FFFFFF>, paste in the offending hyphens (Ctrl-V), then close the html tag with </font>.
4. Click OK to save the results. Thunderbird should automatically detect that you’ve added your own hyphens (albeit invisible ones), and leave you alone.