Has it might be

Hello...

It must be morbidly amusing for the gods of war to hear members of the Obama administration tell the newcomers in Washington that they need a “strategy” to deal with North Korea. After all, painful has it might be for many people to admit, President Obama had no strategy on the North Korea issue. The reason he told Donald Trump that among his biggest problems would be the growing North Korean nuclear and missile programs is because for eight long years the Obama administration’s badly conceived approach failed completely to deal with the issue.

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The underlined part is difficult to grasp the structure of. (Is this correct question sentence?)

Doesn't it have to be, "However painful might it have been ~"?

How come, "has it might" is used there?