Many thanks to you, Laverne. The tip was very useful, but a still better one is found in one of the letters at the end of the program: use TuneUp Utilities 2010. You can download a 30-day trial version. Under the "Customize Windows" header, click on "Appearance of Icons" and uncheck "Show shortcut arrow". Click Apply and restart your computer. The arrows have gone!
Again thank you!