I used to do that to my Mini II about twice a month to remove the slime buildup but if someone could walk me through how to remove the reservoir on my new GS3, I'd appreciate it.

FYI, I did search here and on the web but didn't find any meaningful results.

I've been using a Brita pitcher to pre-filter the tap water going into the reservoir, and on close inspection it's stayed crystal-clear.

The GS/3 Owners Manual (page 10) has cleaning instructions for the reservoir to prevent or fix an algae problem. It's the typical disconnect-disassemble-clean-reassemble routine. I just looked at my machine, and it looks like you need to detach the spring clip on the hose (needle nose pliers should compress the clip) and a small Philips screwdriver will dispatch the reservoir cover. They say it's all machine-washable.

Good luck!