I'm not sure why, but the simpler procedure other answers explain didn't work in my case.
Following this other answer, I had to inspect the page and find the first appearance of an iframe
below the body of the page then take the full class and set it to display: none
.
Here is the CSS code that worked for me on PC using the default Tumblr theme and not logged:
.tmblr-iframe-compact .tmblr-iframe--unified-controls {display:none!important;}
You can find the custom CSS recipient on the "Advanced options" menu.
Additionally, I had to add this other piece of code to make it work on Android:
tumblr_controls, .tmblr-iframe{display:none!important;}
Pay attention because you might not find an easy way to edit your theme anymore, but you can still find the panel by just clikcing on your blog from the dashboard or directly at www.tumblr.com/customize/[yourblog].