Change Block Quote icon with logo

Hi @davidconover,

You can try the code below, but it might require more custom CSS to fit your needs, which is outside the scope of what we’re able to support.
Inside the Customizer open the Additional CSS and paste the following code (replace logo-url.jpg with your logo URL):

.wp-block-pullquote::before {
    content: '';
    background: url(logo-url.jpg);
    background-size: cover;
}

Have a nice day.