Dear Parallels Team,
It’s unacceptable to put ads in a product for which I paid full price (ie Parallels Desktop 7).
Thanks to Google and someone in the Parallels forum for mentioning that the answer is here: NetizenSmith.org.uk. This is a much more palattable place to learn about it compared to needing a Private Message on the Parallels Forum.
Credit to Netizen for finding out that you can type the following in the terminal to remove their ads:
defaults write com.parallels.Parallels Desktop ProductPromo.ForcePromoOff -bool YES