I released the smoke from oscillosope probes, how to repair?
The damage to the insulation is pretty much purely cosmetic. You can either leave it as is, or heatshrink it, it's up to you. Alternatively you could get a new ground clip (they are generally quite cheap), but functionally there will be little difference.



The moral of the story is that ground clips should always be connected to the same potential. If you want to measure two completely independent signals with different ground potentials, you need a differential probe.

You seem to have gotten quite lucky, it is very easy to completely destroy an oscilloscope doing this.