When you import an image directly to the map, there is no symbology options for it. That’s only for items in the legend or symbology tab for legends. That we know. It’s independent graphic images directly onto the map that this happens to.
Under the symbology select "Display Background Value" box and enter the RGB value for the color you want transparent. Leave the background color fill as none.
Regards,
Jim
Apologies, you are adding a picture element to a layout.
How about adding a new dataframe, add the picture to the dataframe as a raster layer, then set the background to transparent. You can also set the dataframe frame to no color, so visually the logo is free floating, as you can move the dataframe and hence the logo where ever you want to on the layout.
Jim