Yes you can filed an amended 2020 Massachusetts income tax return to claim moving expenses on your state return.
As awesome champ @xmasbaby0 said, moving expenses are no longer deductible on your federal return, but you have to enter those expenses in Deductions & Credits in order to get them to flow into state.
For instructions on amending state returns see I need to amend my state return.
For information about deducting moving expenses in Massachusetts see Moving Expense Deduction.
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