You can remove the button part of the code in the email template named "Invoice: Invoice Email". Go to Settings> Tech> Email> Templates (requires developer mode) and look for the name "Billing: Billing Email".

This will open all translations for that email template. Find the language term and edit the Translated Value field. In this column, remove the button part (between% for is_online) statements.

Finally save the translation, reload the page and you'll see that the button is gone from the e-mail now

Regards,
J Wick