This question was put to me. I haven’t found any handy authority to say one way or the other.
My sense is: no. But it may depend. Here’s why:
Usually, if you do things right, the income you earned in Japan is excluded from US taxes through the Foreign Earned Income Exclusion (FEIE). So this excluded income would include the money that you used to pay the Japanese national pension. If Japan turns around and refunds the money, that does not mean it has become different money. It’s the money the government let be excluded through FEIE.
(Alternatively, you could have used money you saved previously to working in Japan to pay the coupons. Then, you clearly had American tax “basis” in the payments that you made to Japan. I know that was the case for me in mid 2005. The refunded payments would clearly be after-tax money, i.e. money that was already taxed by Uncle Sam.)
Simply because Japan withholds 20% of the payment it makes to you as the one-time lump sum (dai tai ichi ji kin), doesn’t mean it’s taxable to America. It would make sense that it might be taxable to Japan–since you got a tax deduction for making the payment. But, even there, Japan will turn around and refund the 20%–which makes no sense.
However, here is the other side: if the IRS decided that the one-time lump sum is a payment to you for foregoing the annuity that you would get from Japan, AND, for whatever specific reasons, the IRS determined that you did not have “basis” in what was contributed to Japan’s pension system, OR that pension payments made by Japan are taxable to you, then you might be on the hook for US taxes.
I kept my pension money with Japan, because—as regular readers know—I consider the lump sum withdrawal to be pre-totalization-era archaism. You are being cheated out of one-half of the value of an annuity at age 65, which is only a deal to you if you know you won’t be around at, (or shortly after), age 65.
I do tax practice now for pay, so I don’t have the, well, situation where I can just do this free internet stuff I’ve done before. If anyone comes across Service guidance, I’ll be happy to update the post.
[Update: this means, obviously, you need the Service to answer that specific.]