Thunderbird shows you the internal "structure" of the HTML you have added. These are the tables that make up the signature that are shown in red. Any time you are editing your signature or editing an email, you will see these red lines, but as soon as you send an email, neither you nor the recipient will be able to see them. If you are concerned we suggest sending an email to yourself as a test, and you will see that the red lines are invisible when you are reading/recieving an email.