The dots come from this part of the CSS:
.nav-menu > li > a:after {
color: #ffa4ad;
content: " \2022";
margin-left: 1em;
}
Specifically, the content declaration, which uses a code from Genericons.
To override that, you’ll need to add something like this to your custom CSS:
.nav-menu > li > a:after {
content: "blah";
}
Replace blah with your new content. You can also use another Genericons code if you like. You can see the codes that are available in the file /fonts/genericons.css
Don’t edit the theme files directly, otherwise your changes will be overwritten whenever the theme is updated.
An easy way to add custom CSS is to install the Jetpack plugin and activate the Custom CSS module. You’ll then add your custom CSS in the new stylesheet editor that’ll appear in your dashboard, under Appearance > Edit CSS.
As alternatives, you could either install a standalone custom CSS plugin, or create a child theme.