Help! Leaving Japan with pending application for pension exemption?

Hello everyone,

I came to Tokyo in late September for a research internship as a graduate student at a big university here. Even though the duration of my stay in Japan is less than 3 months, since I had to officially enroll, I went through the whole process of getting a student visa, residence card, MyNumber, etc. I'm leaving Japan on Saturday and planned to go to the ward office this Wednesday in order to hand them my health insurance card and inform them that I will leave the country.

Today, I got this letter ( https://imgur.com/a/dIb8v1D ) from the National Pension Service saying that, because of my special status as "International Visiting Student" I am not eligible for the special student exemption (over a month after I applied!). There must have been some kind of misunderstanding when I first registered at the ward office in early October, since I just sent them the application form that they gave me (a Japanese tutor from my research group handled all of the stuff at the ward office, I didn't really understand what was going on). They enclosed an application form for the regular exemption. I guess I would be eligible for this one, since I don't have any income, but it seems too late to submit it now, since I leave the country in less than a week.

My Japanese professor suggested I can just ignore the letter, but I will definitely return to Japan as a tourist some day and maybe even live here again in the future. I'm afraid that they will make me pay the full insurance payments on Wednesday. Even though I was just here for less than three months, this is A LOT of money. Any help is appreciated.

TLDR: Special Student exemption application for National Pension was rejected. They sent me an application form for the regular exemption, but I leave the country in less than a week. I don't want to leave Japan with unpaid bills, since I might return someday.

by planemotion