Okay, here's my attempt
. Please try it and give me your feedback.
It has a rather generic icon at the moment (just a square with an "R" in it) so if you feel like doing some graphic design, you could make a new one for it. (It should be somewhere between 32x32 pixels and maybe twice that, but doesn't have to be rectangular. I'd like it to have an empty area in the center where I can superimpose a single-digit number indicating the number of expired reminders.)