Ann Rowan and her research group have just spent some time in the Khumbu Himal investigating debris covered glaciers and the surface ponds that form on them, and here is a BBC article about these features.
Meltwater at the surface of debris-covered glaciers often does not runoff the glacier surface into a stream, but is hemmed in by hillocks and hollows on the glacier surface, and behind large moraines, that at several 100m high are as big as the hills in some parts of the world. This ponded water is pretty important as around the margins of the pond, the warm water and re-radaited long wave radiation from he water surface undercut the ice, and cause blocks of ice to collapse into the lakes. This in itself is a major way in which many dendrites covered glaciers lose ice mass, as the blocks melt into the lake water. Ice cliffs around the lakes also melt much faster than the ice that is buried beneath the rock debris cover and so the amount of exposed ice cliffs around surface ponds might be expected to be a critical control on how fast debris-covered glaciers can lose ice mass.
Look at this picture of an ice cliff at the margin of a pond on the Ngozumpa glacier taken on a real camera in the early 2000s. So much science in here!! You can see how dark the ice cliff is where it is dusted from above, and this dark ice surface will melt much faster than the light grey debris melted ice behind it. You can see the large white overhanging cliff which has recently broken off, slowly being streaked with dirt from above. To the right you can see some impressive debris bands within the ice, and also whats called a thermoerosional notch at the water line, where the movement of warm water against the ice has melted out a notch in the ice cliff. These notches undercut the ice above and cause it to calve off into the pond/lake.
So this fast melting of dark, dusted exposed ice cliffs, and the calving off ob blocks of ice tho the water where they then melt into the pond are the 2 key ways in which ice loss is enhanced around these ponds on top of the glacier surface.