You've just added a new signature in Thunderbird, and when you compose a new message, it has a bunch of red lines around the layout of the signature, like on a screenshot below?
That's okay! Thunderbird uses these red borders to show you where there are HTML tables and cells on which the signature is constructed. The Table itself does not have any pixel border size, so this means you would not see the construction of the Table. However, those are not part of the HTML and won't appear in the sent/received message.
So just compose and send the message, and your recipients won't see these lines: