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What happens if a card tries to move damage counters to the upgraded character?
That effect is ignored. The damage counters stay where they are. They aren’t repaired. If the card trying to move the damage counters has other instructions, those are still followed if possible.
Source: Wave 2 and 3 FAQ
Say for instance that you were playing a full team of Aerialbots, with four planes in vehicle mode. Your opponent played a Strafing Run last turn and spread one damage to each of your characters. Your opponent has a Defensive Driving attached to one of their characters. You play a Bombing Run to move one damage from each of your planes to that character. What happens? Is all damage from Bombing Run dealt with a single damage at a time, per plane you have, or is the damage tallied and then moved in a single chunk? In other words, does that character take three damage from Bombing Run thanks to Defensive Driving, or none at all? Does Defensive Driving block Bombing Run at all, or is "moving" the same as "taking damage"?
Moving damage counters does not count as repairing or taking damage. So Defensive Driving would not block damage in this scenario. Maybe take a look at Bumpers!
Source: Rules Roundup 2019-02-18
If I have a character with Bumpers attached, and I play Involuntary Promotion on a car in my KO area, does the returned character receive the Bumpers in time to prevent the damage counters from being moved?
The damage and upgrades are moved at the same time. Bumpers’ effect won’t stop the damage counters from being moved.
Source: Rules Roundup 2019-11-08