If they paid the bonus in 2017, they are not supposed to issue a corrected 2017 W-2 to remove the bonus.  If they do issue a corrected W-2 for 2017, you simply file an amended 2017 return and if the income is lower, you will owe less tax and get a refund of the excess you paid last year.

If you repaid the bonus in 2018, they could also adjust your 2018 W-2 to reflect that fact -- essentially, deducting the bonus repayment from your final paychecks.  In that case, your 2018 W-2 would show less income and you would file with that and pay the correct tax and you end up even.

If they leave the 2017 W-2 as-is, and the 2018 W-2 is for your actual salary and does not reflect the repayment, then:
If the repayment is less than $3000 you are out of luck.
If the repayment is more than $3000, there is a special procedure to deduct it from your income or take a credit for the excess tax.

I'm not sure there's much point in going into the details until you know if you will get a corrected 2017 W-2 or if the repayment is deducted from your 2018 W-2.

Thank you both for the help. I will include some additional information. I repaid the bonus in 2018 and the amount minus the Social Security and Medicare which I did not have to repay was still greater than $3,000.

I received the following email from my former employer. "Upon repayment, the firm will file a Form W-2C for the year that the wages were included in your W-2. The Form W-2C will reflect a reduction in Medicare wages and, if applicable Social Security wages equal to the amount of taxable income repaid. The Form W-2C WILL NOT change the amount of your federal and applicable state taxable wages or income tax withholdings from the amounts reported on the original W-2.  For additional information, please refer to IRS Publication 525, Taxable and Nontaxable Income, and the instructions to Form W-2C as a reference."

Based on what you said above it looks like I might be eligible to deduct it from my income or take a credit. Is this something I would be able to do with TurboTax myself?

Thanks again!

Since the box 1 taxable wages from 2017 won't change, and assuming they do not deduct it from your 2018 W-2, then you need to use one of the following procedures.

Simple procedure: take a special itemized deduction not subject to the 2% rule.  But, you must itemize already to get the maximum benefit, and the standard deduction was raised by tax reform.  This is listed at the very bottom of the deductions and credits page under "other uncommon deductions."  (You will also recover less tax this way because the tax rates were lowered 2-3% at each bracket, so the deduction will save less than the tax paid previously, in most cases.)

Complex procedure: take a direct tax credit on your 2018 return in the amount that your tax was increased in 2017 due to this money.  This is known as an IRC 1341 Claim of Right.  I can't tell you where to put it on the tax return, because the forms are changing and the IRS has not released the final forms and instructions yet.  You will need to use Turbotax installed on your own computer from a CD or download (and not the Online or Web version) because you will need to make a manual entry on the tax return.  And Turbotax can't calculate the amount of the credit, you will need to do that on your own.  If you have Turbotax 2017 installed on your computer, you could make a test version of your tax return with the lower amount in box 1 of your W-2, and compare your tax due on line 56 of form 1040 with the higher and lower incomes, the difference is the amount of the credit you claim in 2018.

However, the tricky thing about the section 1341 Claim of Right is that to take this credit, you must have had a reasonable expectation at the time you received the money, that you had an unrestricted right to the money.  That means, if you knew you were probably planning to quit in less than 2 years, then you knew or should have known that you should not have accepted the bonus, and you did not have an unrestricted right to it.  But if you legitimately believed you would fulfill the requirements of the bonus, and something unforeseen happened, then you can use the Claim of Right.  (You will want to document this in case of audit.)  If you did not have a reasonable belief to an unrestricted right to the  bonus back when it was paid, you can only use the special itemized deduction, even if it does not allow you to recover all your taxes.

You should check back here after you get your W-2 at the end of January 2019, if you want more help on calculating the credit or how to enter it on your 2018 tax return.

This is a really useful response - I am pretty much in the same boat as the person who posted the original question. One follow up question for you @Opus 17 - "You will need to use Turbotax installed on your own computer from a CD or download (and not the Online or Web version) because you will need to make a manual entry on the tax return." Is there a specific version of Mint I should use or will any version work?

Errata: I meant TurboTax and not Mint.

Thanks for the great response. Now that it is getting closer I would like to buy the software. Would turbotax premier allow you to do a section 1341 claim of right?

Since you need the Desktop version installed on your own computer, any version Deluxe or higher will work.  Deluxe has the same investment and self employment forms as Premier and Home & Business at lower cost, although with less built in assistance.   

Thank you again! I read online that doing this could potentially break the TurboTax Accuracy Guarantee making it impossible to e-file. Do you know if there is any truth to this?

Making manual entries voids the accuracy guarantee, but still allows e-filing.  What also blocks e-filing is making any manual overrides.  I don't believe the IRC 1341 claim requires an override, but it does require a manual entry.

It occurs to me that since Turbotax has announced that Live help is available in all Online versions this year, that if you use the Live Online version, your accountant or CPA you are chatting with may be able to make the manual entry for you, and it might preserve the accuracy guarantee.  I don't know this for sure, Live is a fairly new product and I don't know all the details of how it works.  It is an extra cost add-on compared to the regular Online version.  You can read about it here <a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/3859448-what-is-turbotax-live">https://ttlc.intuit.com/questions/3...> or at the Turbotax home page.  

@Opus 17 - Thank you again for all the help. Now that I am working this out it is making more sense, but has brought up a few more questions.

Does the total tax amount need to be greater than $3,000 or just the amount I repayed to the company including all taxes? The amount I am entering in the form will likely be less than $3,000 but the total repayment was greater.

Additionally, you metioned decreasing the amount in box 1 of my 2017 return to calculate the taxes which I overpayed on line 56 to than use for the 2018 credit. My bonus was taxed at a higher rate so would this impact doing this method?

Lastly, does something separate need to be done for federal and state or does entering the total amount in the form take care of both?

Thanks again for all the help!

The repayment must be more than $3000--the amount of the check you write to your former employer.
 
Bonuses are withheld at a higher rate but at the end of the year they are taxed along with your regular income.  The credit amount, if you figure it manually, is whatever different the bonus made in the year you received it.  Because the tax rates were reduced, it is likely that your bonus might have been taxed at 15% or 25% last year, even though the tax rates are 12% and 22% this year.  Thats ok.  The amount of the credit is whatever extra tax you paid last year because of the bonus you are now repaying.

If you use the itemized deduction method, that probably automatically takes care of the state since your itemized deductions usually flow from federal to state (for most "conforming" states).  If you use the IRC1341 Claim of Right credit, that does not go to the state form.  You would have to ask your state or check their web site or instructions, to see what their procedure is (if they have one) for salary repayments.

Now the 2018 publication 525 is out. On page 34 we have "If method 1 results in less tax, deduct the
amount repaid. If method 2 results in less tax, claim the credit figured in (3) above on Form 1040.", but I am still not quite sure at which line on the form 1040 should I put this credit, and how should I do that in TurboTax. Help appreciated!

@Opus 17 Now that I am ready to file I just want to make sure I have understood everything correctly.

I went to my 2017 TurboTax Desktop program and dropped the income in box 1 - Wages by the total amount that I repaid. I then took the new number in the Federal Refund box and subtract the old number from it. This is the amount that I enter into the form 1040 in the forms mode on my 2018 return by doing the following:

"Go to FORMS (top right of main screen) > Form 1040 > Scroll below line 72 to "Other Payments and Credits Smart worksheet"
Please enter the credit in line D.
This credit should show up on Form 1040 line 73"

Please let me know if I have understood this correctly. I have also tried the deduction method but received the notice that the standard deduction is the best option.

Thanks again for all the help!