I assume the problem is you can’t register it in MA. Could you just sell it? Seems strange to me.

You need to get a copy of the actual rules and carefully read them, line by line.
Are they saying any car bought in MA and then brought back to MA after being in another state must pay the original tax?
That does seem unfair.
Knowing MA it is probably a tax first ask questions later. I would hope they allow you to prove you were an actual resident of NH and legally not obligated to pay sales tax.
I can understand if someone bought a car reg. in NH and then 60 days later reg, in MA and they could not prove NH residence.
Go back to the dealer, they know how the system works.
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PS Go to the RMV web site. They have some notes on this. It looks like if you had your vehicle delivered to you in MA, ie that was your address when you bought the car, they may have you.