How to say "damage control" (to minimize damage to reputation)
In the navies and the maritime industry, damage control is the emergency control of situations that may cause the sinking of a watercraft. It is translated as 损害控制 (damage control).
损害控制 can also be used metaphorically for &quot;preventing damages to become more severe&quot;
Example:
The White House staffers have to do damage control for the president's deranged tweets almost every day --&gt; 白宫人员几乎每天都要对总统失控的推文进行损害控制. Metaphorically compare the damage caused by the president's tweets to ship-sinking damage (the damage is done, all you can do is not letting the ship sinks).
It would be easier in Cantonese -- 白宫人员几乎日日都要帮总统失控嘅推文补镬.

(to minimize damage to reputation)

The term 公关补救 (PR remedy) seems to fit
We can use a Cantonese slang 解畫 for that -- a metaphor for &quot;to spin; to explain away the problem&quot; I am not sure it is used in Mandarin or not