Remove blavatar CSS to anon user

Hello,

Is there an available function that we might be able to call in our theme to remove head CSS relating to blavatars:

#wpadminbar .quicklinks li#wp-admin-bar-blog-X .blavatar {}

We believe there is no need to serve this CSS to anonymous users.

Thanks for your help and the great plugin!

https://wordpress.org/plugins/multisite-enhancements/