Unfortunately, we cannot control what email signatures look like after someone replies to our emails. That's because once the signature leaves our own email client, there are so many other factors that can affect the signature, that we cannot control.
When the signature arrives in the recipient's email client, and is read by the recipient, it should look as it's intended to look* because that recipient is in "reading mode".
But as soon as that recipient hits reply to your email, the recipient's email client has just changed to "composing mode". The user and the user's email client can now alter the HTML in your signature however they like or need.
For example, the user may have settings to reply only in plain text in their email client, which would strip out the HTML and show only the code or plain text. Or the user's email client may strip images on reply and take out the images from your email signature. There's a lot of things that can happen and we cannot control any of them at this point.
There is no solution or workaround for this when using HTML email signatures. It's just the way that email clients work.
*Email Signature Rescue conducts extensive cross-email-client compatibility testing on all of our email signature templates to ensure that we have the best code possible to work across all of the major (and many of the minor) email clients that support HTML. Most recipients will see the email signatures as they are intended to look, if they are using any of our supported email clients, however we can never guarantee that your signature will always look as intended, as that is controlled at the destination, not at the source.