Fjellrev
I don't know if there are any sources in english nor how good you understand german but I found these links that describe the situation:
https://de.wikipedia.org/wiki/Unterer_Grindelwaldgletscher
http://www.gletschersee.ch/index.cfm?treeID=18
The glacier has melted quite a lot - this is correct and it might be redrawn if one gets good sources (I haven't checked Bing lately) - but beneath Bäregg there is still a glacier. It is not connected to the higher glaciers anymore (We call it Toteis "dead ice" in german), the lake lies actually on top of the ice which is covered with stones.
This makes aerial pictures like Bing kind of useless to really see where the glacier begins and where it ends. :-(