It appears you cannot add or remove picture elements using ArcPy. If it's acceptable you can use a work around and set the element height to 0.
pict = arcpy.mapping.ListLayoutElements(mxd, "PICTURE_ELEMENT")
pict.elementHeight = 0
Here's a red bar picture element which disappears once I set its height to zero. It sounds like you're working outside the ...
Give this a try (from a GeoNet post)
Open internet explorer and got to the tools, click on internet options, then Connections then LAN Settings. Uncheck the option that says Automatically detect settings. Basically the problem was that the basemap was searching for the host site through all my local networks and unchecking this option bypasses that.