This topic only applies to older display templates running WebForms type. Newer templates using Razor type makes this step very easy.
You can safely delete any unwanted HTML elements but never delete any server-side ASP.NET elements (elements that begin with "asp:" prefix) as these server controls are needed by the application to run.
For example, you can delete the <a href="/somewhere" /> because this is just a plain regular HTML element, however, you should not delete <asp:HyperLink runat="server" NavigateUrl="/somewhere" />.
Instead, you should use CSS to hide the unwanted ASP.NET elements. For example, you can add the style="display:none" or style="visibility:hidden" to the ASP.NET element.
<asp:Label ID="SavingsValueLabel" runat="server" style="display:none" />
<div style="visibility:hidden" />