You pose an interesting question, and I did some tax research on it for you. Here is what I found.
According to the (Bloomberg) BNA Tax Management International Journal, Vol 33, No. 3, p. 153, current taxation in the Marshall Islands allows the local government there to impose personal income taxes on private contractor US citizens working in the RMI, although the tax may not be mandatory.
The Marshall Islands is treated as a foreign country by the IRS for personal income taxation, so any local RMI income taxes you may have paid to the Marshall Islands while you were working there (which may be shown on your W-2, in Box 17), potentially could be then claimed as a foreign taxes paid credit, through the foreign earned income process set out under IRS Form 2555. However, in order to do that, you would need to meet either the Physical Presence Test or the Bona Fide Resident Test, which are explained in detail here at the following IRS.gov webpage:
https://www.irs.gov/instructions/i2555/ch02.html
Basically, though, if you were living in the Marshall Islands for less than a full-year, you won't qualify for this particular tax benefit. But if you think that you do, in TurboTax, you'll want to search for the exact term "foreign earned income exclusion" in the Find / Search box of your open TurboTax return. You also would probably have to upgrade from your current (Free) edition of TurboTax into a paid version, just to access Form 2555, although the software would let you know that. (A screen-capture image of this process is attached to the bottom of this answer for visual reference.)
As to what to do with your W-2 statement (with Box 15 printed as RMI), please do the following. This is how you should mechanically enter it in TurboTax. Begin with the W-2 tax data just as you have it on your printed document, and continue until you reach Box 15. Then, in Box 15, change RMI to the 2-letter abbreviation corresponding to your home state of residence (i.e., legal domicile). For example, if your home is California, you will enter CA from the drop-down menu. Next, use the same number from W-2 Box 1, and type that same number into Box 16. Then leave Box 17 completely blank (even if Box 17 shows a number on your actual paper statement). At that point you can stop.
If Box 17 shows an income tax withholding value for RMI, then this is the number you would use for figuring your foreign taxes paid figure, for purposes of filling out the foreign income exclusion calculation in Form 2555 (as just described above).
Basically, what we are doing here is ensuring that your W-2 conforms to IRS reporting standards; and also making sure that your W-2 wages are reported, and taxable, to your home state (if your home state indeed has a personal income tax, like California; if your home state does not have a personal income tax, like Florida, then this portion of the discussion is not necessary).
That process, outlined above, should take care of proper income tax reporting. Additionally, if you wish, here is a link to the BNA foreign tax research publication, which constitutes much of my research source material.
http://www.parsonsbehle.com/publications/taxation-of-individuals-in-united-states-possessions
While all this information may seem like a lot to absorb, it is my belief as a practicing CPA that it is accurate and correct.
Thank you for asking this important question.
