That's because you are sending the invite to an existing client who had already accepted the Link invite previously.  In this case, a different email template is used to notified your client that the checklist has been updated with new item(s).

Don't believe you can choose a different template to use or edit the message for existing clients if you send it from within Lacerte.  But if you log into Link for Accountants, you can create your own templates for client notification under Firm Settings > Email Templates > +New Template.

Whenever you create a new request and click on the button to send it (i.e. not Send Without Email), you can then choose which template to use and edit the content as you see fit.