This is the custom css I had been using, with details edited to fit my site (sizing, etc). I re-entered it fresh, added my image url, and the dots remained.
I started playing around with sizing and for some reason setting the font-size at 2em and margin-top at .01em made the dots disappear. No clue why but I am taking this as a win! I hope this helps someone else.
/*Add logo to display in mobile*/
#mobile-navigation-title a {
color: transparent;
background-image: url("YOUR_IMAGE_URL_HERE");
background-size: contain;
background-position: center;
background-repeat: no-repeat;
font-size: 2.5em;
}
/*Adjust mobile hamburgernav position*/
#mobile-navigation-label {
margin-top: 1em;
}