Well, I'm optimistic hearing from you guys that losing these links may not cause us a rankings apocalypse, but I've also got to admit that I'm a bit disheartened that a strategy like this wouldn't have been as powerful in the first place as I thought. I didn't know that "powered by" links had been targeted by Google, and for so long, too.
To be clear: the words "powered by ________" are contained in the image, so the text "powered by" doesn't actually appear in the source. But the vast and consistent placement across thousands of pages... I'm sure their algorithms were able to figure it out. If it makes a difference, the link was fairly visible on the page--above the fold, not in the footer or sidebar or anything.
Anyhow, they'll be going away within the next 60-90 days, so I'll try to follow up with a post about any effects/non-effects that this has. If anyone comes across this thread several months from now and I haven't posted results, post a reply here and I'll update you all with the results. But I'll also try to remember to update the thread in the weeks following the links coming down.