To start the process navigate to Toolbox - Form Manager and search for newsletter_modal_signup

Customize the form by selecting this option from the dropdown menu:

Once inside the form, open the form Field Settings and use the Show in  Email View to decide whether or not this field should be included in the email. 

By default new custom fields show up with this email setting set to Yes, follow this process to switch it to No if the field does not need to be included in emails.