To clarify, I was able to duplicate this in BLS-2016 version 28.05.05.
Brendan, you should post your version number with your questions, as the version may contain an issue that's since corrected, or that developed post-release.
Both with and without a league open, the Help menu has these gray bars that Brendan describes, and I find the same behavior in both cases (league open and not open).
Granted, the gray bars are quite thin, but if the mouse pointer is appropriately placed, this can occur just the same. Are the gray bars necessary, and/or can they be re-coded to result in no action at all (ignore the click and keep the list of menu items visible and active)?
At the very least, pressing ESC or ENTER will dismiss the error dialog, but the menu disappears and the menu heading must be re-clicked (necessitating moving the mouse pointer back up to the top, and then back down to the desired item).
Finally, back to Brendan: If you are frequently using the Help menu, you may be able to put whatever item(s) under that menu into "My Menu" and click there instead. In short, that could be a workaround. I realize a Standard version of BLS-2016 only allows a few "My Menu" items, with a Pro version offering many more, but it's a thought.
Always check, download, and install the most recent update of your software to ensure that issues may have been corrected.