It can cause signal chain saturation and at the very least carries a settling time penalty which becomes increasingly relevant as we read faster. Having never heard of a way to reduce it, I assumed that it was an inescapable feature of CCDs. I had been thinking of it as a narrow positive going pulse - the way it looks on the oscilloscope. This led me to adjust the high level of Reset Gate. This has no effect since the output node is connected to Reset Drain while RG is high.
Charge is shared between it and the CCD output node.
I saw your message about reset feedthrough. Linearity doesn't depend on such small changes, at least in my experience.