Hello again!
I checked, and this arrow is present in the Mate-Ambient theme in Ubuntu MATE 16.04. I never noticed this until you mentioned it! Maybe there will be a patch to remove it in a future update.
Unfortunately, I do not know of a solution that does not involve code. But the following solution did work for me:
First, I created an empty file entitled: .gtkrc-2.0 in my home directory. See:
https://ubuntuforums.org/showthread.php?p=6364278#post6364278
Next, I pasted the code from this post into the .gtkrc-2.0 file: https://ubuntuforums.org/showthread.php?t=1010435&p=6364434#post6364434
Next, I saved the .gtkrc-2.0 file.
Finally, I changed to a different theme, and then changed back to the theme I actually wanted to use, as described here: https://ubuntuforums.org/showthread.php?t=1010435&p=6364278#post6364278
Hope that helps!