If, as you say, the theme does not provide direct show/hide configuration options, your most typical choices will be, I think:
1) If the theme provides a CSS class enabling targeting of the view count as rendered, to make it disappear via CSS;
2) If the theme provides a filter for rendering the view count, make it disappear with a custom function;
3) Edit as many of the template files as necessary, with the relevant code removed or replaced.
Though, in the case of #1, you might be able to achieve the effect with an independent CSS processor (like JetPack Edit CSS, for example), it’s best practice to perform alterations in a child theme, so as to avoid losing them during upgrades, and (as is seldom noted!), if you are going to perform multiple customizations over time, to keep them organized and set apart in one place.