The most straightforward fix for Gravatar-related warnings in PageSpeed Insights is to disable avatars. If you need to keep avatars in some locations, there are a few options available:
WP User Avatar
Gravatar Cache
Note that we don’t recommend this, however, as we’ve heard reports from clients that server-side performance issues exist.
Lazy Load for Comments
Note that we’ve experienced issues when both pagination and this plugin are enabled. We recommend only enabling pagination OR comment lazy loading.
Hard-code images in your theme
If you’ve disabled avatars, they can be manually re-added through your theme. Though we don’t have an article on this currently, let us know if you’re interested and we’ll put one together for you!