This is because your logo is a small GIF and looks fine on a desktop at its native dimensions. However in mobile mode Gantry widens that container to a 100% to follow responsive guidelines so your low quality image gets scaled and thus looks pixellated.
To force the logo container back to native image dimensions, in your
[JOOMLA-ROOT]/templates/rt_ambrosia/custom/scss/custom.scss (<--CLICK this is link)
file add this:
@media only all and (max-width: 47.938rem) {
#g-header .g-logo img {
width: 70%;
}
}