Add the class u-no-print to elements you want to hide when the page is printed.
Use your browser's print preview to see the following example working.
To import just this utility into your project, copy the snippet below and include it in your main Sass file.
// import Vanilla and include base mixins
// this only needs to happen once in a given project
@import 'vanilla-framework';
@include vf-base;
@include vf-u-no-print;
For more information see Customising Vanilla in your projects, which includes overrides and importing instructions.