Add a white background behind logo in mobile overlay

Add to Design > Custom CSS

@media screen and (max-width:767px) {
.header-menu-bg.theme-bg--primary {
    background-color: white !important;
}
.header-menu-nav {
    background-color: var(--menuOverlayBackgroundColor) !important;
}
body.header--menu-open .burger-inner>div {
    background-color: var(--menuOverlayBackgroundColor) !important;
}
}