You have three states involved, so I'll try to give guidance on each. My answer presumes that your job is located in Massachusetts, but if that is not correct please let me know.
Massachusetts: You are a resident of Massachusetts, so all of your income is taxed in Massachusetts no matter where you earned it. When income is taxed in Massachusetts and another state, Massachusetts will allow you to claim a credit for tax you must pay to the other states on income earned there. Because of this credit, always prepare Massachusetts last.
Missouri: Do not correct the W-2. If the company made a mistake and over-withheld Missouri tax, you must file a Missouri nonresident return receive a refund of any excessive withholdings. If the actual income reported on the W-2 for Missouri is not accurate, you can use Missouri tax screens to correct the amount to the actual amount you earned while physically in Missouri. Prepare this return first.
Maine: It depends and it's complex. The first issue is whether or not you are a statutory resident of Maine. If you spent 183 days or more in Maine, and you owned a residence (a vacation home is a residence), then you would be considered a statutory resident of Maine, which would require you to file a Maine resident tax return. If that is the case, then all of your income is taxable in Maine, but then any tax you must pay to Maine can be (potentially) claimed as a credit on your Massachusetts return). And the tax you pay to Missouri is a credit on your Maine return, to reduce the Maine tax somewhat. If this is your situation, prepare this return second, and use the Maine income (should be the same as the Federal amount), as well as the tax due to Maine for the out-of-state tax credit on the Massachusetts return.
However, if you do not meet the definition of a statutory resident, then you shouldn't need to file a Maine return at all. Due to the temporary tax provisions the state adopted during the coronavirus emergency, Maine was not requiring other states to withhold Maine tax on Maine residents who were telecommuting from their Maine home for an out-of-state employer. The income of these workers is still taxable in Maine (as Maine residents), but the income is considered as priority-taxed in the state where the employer is located, and Maine would issue a credit against that (again, for Maine residents). But the way the provision reads would mean that a nonresident physically working in Maine, but teleworking for a company located outside of Maine, is not generating income that is taxable to Maine. So if you are not a statutory resident of Maine, it would appear you do not need to report any of this income to Maine at all. The best source of information on this (and it's not 100% clear, mind you), is found at this link: MAINE TAX ALERT - Maine.gov
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