Please excuse my passing on this information to you. I am obviously not IAAL. Here is my two cents worth of free legal advice.
First, your employer can't make you re-pay the overtime pay that you have already received. It appears that they agree with you that said overtime pay was properly given to you. That said overtime pay was given to you in conformity with the Fair Labor Standards Act (FLSA). Thus, that money is your own personal property that you obtained in exchange for your previously provided work.
Second, any pay raise that is to be given to you retroactively is for an increase in the base or hourly rate. Said pay raise has no effect on whether the employer was obligated to pay you for overtime per the FLSA.
For more information on the FLSA, you can go to
freeadvice.com/gov_material/dol-reference-guide-to-fair-labor-standards-act.htm.
Another site is at
job-law.com/article/overtime_pay.htm.
I hope this helps! Perhaps even professor IAAL will smile upon this advice.
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Mark B. Replogle
