Good enough to get a visual orientation. The capacitor marked 681 corresponds to C1203 in channel 1. From there VC1203 and VC1204 were sorted out by other clues.
This is the attenuator for ranges .5 1 and 2.
What I'm proposing will be highly sacrilegious to some purists, so it may be better for some people to turn their heads and look way.
A good practice before making adjustments is to make a small vertical mark over the edge and side of each trimmer capacitor to identify the original position. A 0.5mm pencil is good. Wherever accessible, mark all of the capacitors.
Using the only square wave source available, the built-in calibrator, let's see what can be accomplished with the attenuator compensation. Connect the calibrator signal to the channel 1 input with just a piece of wire. Set the range to .5 volts per division. This should produce about a 2 division vertical signal.
Using the little plastic tweaker that came with the new probes, try adjusting VC1203 to see what improvement can be made to the overshoot. Work back and forth between VC1203 and VC1204 to obtain the best looking square corner, free of overshoot or rounding, just as is done for scope probes.
A note about VC1204, this control can go through multiple revolutions so it will be necessary to keep track of the turns.
In the event no improvement can be obtained, then it would be best to reset these trimmers to their original positions.
Ideally - these adjustments should be done as macboy described. Let's just see what can be done with bailing wire and ten-penny nails, as it were.
Edited to add:
VC1202, VC1204 and VC1206 establish the scope's input capacitance. In practice, these are all set to the same value with a capacitance meter.
Therefore, it is best not to alter VC1204 at this time.
RF+ Tech